The On-Line Encyclopedia of Integer Sequences (OEIS)

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A126694

Expansion of g.f.: 1/(1 - 7*x*c(x)), where c(x) is the g.f. for A000108.
(history; published version)

#17 by Charles R Greathouse IV at Thu Sep 08 08:45:29 EDT 2022

PROG

(MAGMAMagma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(7*Sqrt(1-4*x) -5) )); // G. C. Greubel, May 05 2019

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#16 by Vaclav Kotesovec at Mon Nov 29 04:08:35 EST 2021

STATUS

editing

approved

#15 by Vaclav Kotesovec at Mon Nov 29 04:08:25 EST 2021

FORMULA

a(n) ~ 5 * 7^(2*n) / 6^(n+1). - Vaclav Kotesovec, Nov 29 2021

STATUS

approved

editing

#14 by Susanna Cuyler at Sun May 05 09:13:22 EDT 2019

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proposed

approved

#13 by Michel Marcus at Sun May 05 01:24:40 EDT 2019

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editing

proposed

#12 by Michel Marcus at Sun May 05 01:24:24 EDT 2019

EXTENSIONS

a(16) corrected by G. C. Greubel, May 05 2019

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proposed

editing

#11 by G. C. Greubel at Sun May 05 00:16:51 EDT 2019

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editing

proposed

#10 by G. C. Greubel at Sun May 05 00:13:16 EDT 2019

NAME

GExpansion of g.f.: 1/(1 - 7*x*c(x)), where c(x) is the g.f. for A000108.

DATA

1, 7, 56, 455, 3710, 30282, 247254, 2019087, 16488710, 134656130, 1099686056, 8980749862, 73342721956, 598965319960, 4891549246290, 39947649057855, 3262391226611830, 326239122661830, 2664286127154330, 21758336553841440, 177693081299126610

LINKS

G. C. Greubel, <a href="/A126694/b126694.txt">Table of n, a(n) for n = 0..1000</a>

MATHEMATICA

CoefficientList[Series[2/(-5+7*Sqrt[1-4*x]), {x, 0, 30}], x] (* G. C. Greubel, May 05 2019 *)

PROG

(PARI) my(x='x+O('x^30)); Vec(2/(7*sqrt(1-4*x) -5)) \\ G. C. Greubel, May 05 2019

(MAGMA) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 2/(7*Sqrt(1-4*x) -5) )); // G. C. Greubel, May 05 2019

(Sage) (2/(7*sqrt(1-4*x) -5)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 05 2019

STATUS

approved

editing

#9 by Bruno Berselli at Sun Jul 24 10:47:58 EDT 2016

STATUS

proposed

approved

#8 by Joerg Arndt at Sun Jul 24 06:45:32 EDT 2016

STATUS

editing

proposed