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A259547
a(n) = n^4*Fibonacci(n).
2
0, 1, 16, 162, 768, 3125, 10368, 31213, 86016, 223074, 550000, 1303049, 2985984, 6654713, 14482832, 30881250, 64684032, 133383037, 271257984, 544872101, 1082400000, 2128789026, 4148908016, 8019403537, 15383789568, 29306640625, 55473687568, 104384578338
OFFSET
0,3
LINKS
FORMULA
G.f.: -x*(x^8-11*x^7+87*x^6-48*x^5+240*x^4+48*x^3+87*x^2+11*x+1) / (x^2+x-1)^5.
E.g.f.: exp(x/2)*x*(5*(1 + 7*x + 12*x^2 + 3*x^3)*cosh(sqrt(5)*x/2) + sqrt(5)*(1 + 21*x + 24*x^2 + 7*x^3)*sinh(sqrt(5)*x/2))/5. - Stefano Spezia, Aug 25 2024
MAPLE
a:= n-> n^4*(<<1|1>, <1|0>>^n)[1, 2]:
seq(a(n), n=0..50); # Alois P. Heinz, Jun 30 2015
MATHEMATICA
Table[n^4 Fibonacci[n], {n, 0, 30}] (* or *) LinearRecurrence[{5, -5, -10, 15, 11, -15, -10, 5, 5, 1}, {0, 1, 16, 162, 768, 3125, 10368, 31213, 86016, 223074}, 30] (* Harvey P. Dale, Mar 09 2016 *)
PROG
(PARI) a(n) = n^4*fibonacci(n)
(PARI) concat(0, Vec(-x*(x^8 -11*x^7 +87*x^6 -48*x^5 +240*x^4 +48*x^3 +87*x^2 +11*x +1)/(x^2 +x -1)^5 + O(x^50)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jun 30 2015
STATUS
approved