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A155952 A triangle of polynomial coefficients: q(x,n)=-((x - 1)^(2*n + 1)/x^n)*Sum[(2*k + n)^n*Binomial[k, n]*x^k, {k, 0, Infinity}]; p(x,n)=q(x,n)+x^n*q(1/x,n). 0
2, 4, 4, 48, 48, 728, 232, 232, 728, 20752, 5312, 1632, 5312, 20752, 759132, 168684, 39864, 39864, 168684, 759132, 34016320, 5788288, 3904448, -2262272, 3904448, 5788288, 34016320, 1801010416, 223429840, 253864944, -64253360, -64253360 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are:

{2, 8, 96, 1920, 53760, 1935360, 85155840, 4428103680, 265686220800,

18066663014400, 1373066389094400,...}.

LINKS

Table of n, a(n) for n=0..31.

FORMULA

q(x,n)=-((x - 1)^(2*n + 1)/x^n)*Sum[(2*k + n)^n*Binomial[k, n]*x^k, {k, 0, Infinity}];

p(x,n)=q(x,n)+x^n*q(1/x,n);

t(n,m)=coefficients(p(x,n))

EXAMPLE

{2},

{4, 4},

{48, 48},

{728, 232, 232, 728},

{20752, 5312, 1632, 5312, 20752},

{759132, 168684, 39864, 39864, 168684, 759132},

{34016320, 5788288, 3904448, -2262272, 3904448, 5788288, 34016320},

{1801010416, 223429840, 253864944, -64253360, -64253360, 253864944, 223429840, 1801010416},

{110076993792, 8135276544, 21010185216, -9977444352, 7196198400, -9977444352, 21010185216, 8135276544, 110076993792},

{7625557131380, 185854731220, 1792122898960, -827150318000, 256947063640, 256947063640, -827150318000, 1792122898960, 185854731220, 7625557131380},

{590491073741824, -15412908181504, 169164874601472, -90458315169792, 50709230659584, -35921522208768, 50709230659584, -90458315169792, 169164874601472, -15412908181504, 590491073741824}

MATHEMATICA

Clear[p, x, n, m];

p[x_, n_] = -((x - 1)^(2*n + 1)/x^n)*Sum[(2*k + n)^n*Binomial[k, n]*x^k, {k, 0, Infinity}];

Table[FullSimplify[ExpandAll[p[x, n]]], {n, 0, 10}];

Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]

+ Reverse[ CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x]], {n, 0, 10}];

Flatten[%]

CROSSREFS

Sequence in context: A225171 A320600 A290606 * A277445 A145636 A334190

Adjacent sequences:  A155949 A155950 A155951 * A155953 A155954 A155955

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Jan 31 2009

STATUS

approved

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Last modified May 22 05:51 EDT 2022. Contains 353933 sequences. (Running on oeis4.)