A304781 - OEIS

A304781

a(n) = [x^n] (1/(1 - x)^n)*Product_{k>=1} (1 + x^k).

1, 2, 6, 21, 75, 274, 1016, 3807, 14377, 54627, 208584, 799669, 3076167, 11867511, 45897145, 177888715, 690770763, 2686879415, 10466761637, 40828165464, 159453481037, 623427464093, 2439907421914, 9557831470082, 37472409664888, 147028505564603, 577302980976146

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OFFSET

0,2

COMMENTS

Number of partitions of n into odd parts with n + 1 kinds of 1.

LINKS

Table of n, a(n) for n=0..26.

Index entries for sequences related to partitions

FORMULA

a(n) = [x^n] (1/(1 - x)^n)*Product_{k>=1} 1/(1 - x^(2*k-1)).

a(n) = [x^n] (1/(1 - x)^n)*exp(Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k))).

a(n) ~ QPochhammer[-1, 1/2] * 4^(n-1) / sqrt(Pi*n). - Vaclav Kotesovec, May 18 2018

MATHEMATICA

Table[SeriesCoefficient[1/(1 - x)^n Product[(1 + x^k), {k, 1, n}], {x, 0, n}], {n, 0, 26}]

Table[SeriesCoefficient[1/(1 - x)^n Product[1/(1 - x^(2 k - 1)), {k, 1, n}], {x, 0, n}], {n, 0, 26}]

Table[SeriesCoefficient[1/(1 - x)^n Exp[Sum[(-1)^(k + 1) x^k/(k (1 - x^k)), {k, 1, n}]], {x, 0, n}], {n, 0, 26}]

Table[SeriesCoefficient[QPochhammer[-1, x]/(2 (1 - x)^n), {x, 0, n}], {n, 0, 26}]

CROSSREFS

Cf. A000009, A036469, A095944, A128566, A128593, A292463, A292613, A293467.

Sequence in context: A263790 A247416 A105872 * A148490 A006612 A116769

Adjacent sequences: A304778 A304779 A304780 * A304782 A304783 A304784

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, May 18 2018

STATUS

approved