A296775 Expansion of 1/Sum_{k>=0} A000326(k+1)*x^k.

1, -5, 13, -27, 54, -108, 216, -432, 864, -1728, 3456, -6912, 13824, -27648, 55296, -110592, 221184, -442368, 884736, -1769472, 3538944, -7077888, 14155776, -28311552, 56623104, -113246208, 226492416, -452984832, 905969664, -1811939328, 3623878656

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..3316

Wikipedia, Pentagonal number

Index entries for linear recurrences with constant coefficients, signature (-2).

Formula

a(n) = -2*a(n-1) for n > 3.

For n >= 3, a(n) = (-1)^n * 27 * 2^(n-3). - Vaclav Kotesovec, Dec 20 2017

G.f.: (1-x)^3/(1+2*x). - Robert Israel, Dec 20 2017

E.g.f.: (1/8)*(- 19 + 14*x - 2*x^2 + 27*exp(-2*x) ). - Alejandro J. Becerra Jr., Feb 16 2021

Maple

1, -5, 13, seq(-27*(-2)^i, i=0..50); # Robert Israel, Dec 20 2017

Mathematica

CoefficientList[Series[1/Sum[(k+1)*(3*k+2)*x^k/2, {k, 0, 30}], {x, 0, 30}], x] (* Vaclav Kotesovec, Dec 20 2017 *)
Join[{1, -5, 13}, Table[(-1)^n * 27 * 2^(n-3), {n, 3, 30}]] (* Vaclav Kotesovec, Dec 20 2017 *)

Prog

(PARI) N=66; my(x='x+O('x^N)); Vec(1/sum(k=0, N, (k+1)*(3*k+2)/2*x^k))
(PARI) first(n) = Vec((1-x)^3/(1+2*x) + O(x^n)) \\ Iain Fox, Dec 20 2017
(Magma) [1, -5, 13] cat [-27*(-2)^(n-3): n in [3..50]]; // G. C. Greubel, Jan 04 2023
(SageMath) [1, -5, 13]+[-27*(-2)^(n-3) for n in range(3, 51)] # G. C. Greubel, Jan 04 2023

Crossrefs

Cf. A000326, A294372.

Sequence in context: A079989 A062480 A027024 * A272045 A248860 A185039

Adjacent sequences: A296772 A296773 A296774 * A296776 A296777 A296778

Keyword

sign

Author

Seiichi Manyama, Dec 20 2017

Status

approved