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A296817 Expansion of 1/Sum_{k>=0} (2*k+1)^2*x^k. 0
1, -9, 56, -328, 1912, -11144, 64952, -378568, 2206456, -12860168, 74954552, -436867144, 2546248312, -14840622728, 86497488056, -504144305608, 2938368345592, -17126065767944, 99818026262072, -581782091804488, 3390874524564856, -19763465055584648 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (-6,-1).

FORMULA

a(n) = -6 * a(n-1) - a(n-2) for n > 3.

For n > 1, a(n) = 4*(-1)^n * ((sqrt(2)+1)^(2*n-1) - (sqrt(2)-1)^(2*n-1)). - Vaclav Kotesovec, Dec 21 2017

G.f.: (1-x)^3/(1+6*x+x^2). - Robert Israel, Dec 21 2017

a(n) = 8*A002315(n-1), n>1. - R. J. Mathar, Jan 27 2020

MAPLE

f:= gfun:-rectoproc({a(n) = -6 * a(n-1) - a(n-2), a(0)=1, a(1)=-9, a(2)=56, a(3)=-328}, a(n), remember):

map(f, [$0..50]); # Robert Israel, Dec 21 2017

MATHEMATICA

CoefficientList[Series[1/Sum[(2*k+1)^2*x^k, {k, 0, 30}], {x, 0, 30}], x] (* Vaclav Kotesovec, Dec 21 2017 *)

f[n_] := Simplify[ 4*(-1)^n*((Sqrt[2] +1)^(2n -1) - (Sqrt[2] -1)^(2n -1))]; f[0] = 1; f[1] = -9; Array[f, 22, 0] (* or *)

CoefficientList[ Series[-(x^3 -3x^2 +3x -1)/(x^2 +6x +1), {x, 0, 21}], x] (* or *)

Join[{1, -9}, LinearRecurrence[{-6, -1}, {56, -328}, 20]] (* Robert G. Wilson v, Dec 21 2017 *)

PROG

(PARI) N=66; x='x+O('x^N); Vec(1/sum(k=0, N, (2*k+1)^2*x^k))

CROSSREFS

Cf. A016754, A115291.

Sequence in context: A026863 A026890 A163889 * A034362 A037711 A037613

Adjacent sequences:  A296814 A296815 A296816 * A296818 A296819 A296820

KEYWORD

sign,easy

AUTHOR

Seiichi Manyama, Dec 21 2017

STATUS

approved

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Last modified March 4 00:34 EST 2021. Contains 341772 sequences. (Running on oeis4.)