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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 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.)