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 A154337 A triangular sequence of coefficients of polynomials: p(x,n)=(3*(x - 1)^(n)*Sum[(((-1)^(n)*(2*k + 1)^(n - 1)))*x^k, {k,0, Infinity}] -(x - 1)^(n + 1)*Sum[((-1)^(n + 1)*k^n)*x^k, {k, 0, Infinity}]/x)/2. 2
 1, 1, 1, 1, 7, 1, 1, 29, 29, 1, 1, 101, 312, 101, 1, 1, 327, 2372, 2372, 327, 1, 1, 1023, 15219, 34114, 15219, 1023, 1, 1, 3145, 88839, 381775, 381775, 88839, 3145, 1, 1, 9577, 490114, 3683815, 6934426, 3683815, 490114, 9577, 1, 1, 29003, 2610590, 32334362, 103464764, 103464764, 32334362, 2610590, 29003, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row sums are: {1, 2, 9, 60, 516, 5400, 66600, 947520, 15301440, 276877440,...} LINKS G. C. Greubel, Table of n, a(n) for n = 0..1274 FORMULA p(x,n)=(3*(x - 1)^(n)*Sum[(((-1)^(n)*(2*k + 1)^(n - 1)))*x^k, {k,0, Infinity}] -(x - 1)^(n + 1)*Sum[((-1)^(n + 1)*k^n)*x^k, {k, 0, Infinity}]/x)/2. Functional form: p(x,n)=(3*(-1)^n* 2^(-1 + n)* (-1 + x)^n* LerchPhi(x, 1 - n, 1/2) - (-1)^(1 + n) *(-1 + x)^(1 + n)* PolyLog( -n, x)/x)/2. t(n,m)=Coefficients(p(x,n)) EXAMPLE {1}, {1, 1}, {1, 7, 1}, {1, 29, 29, 1}, {1, 101, 312, 101, 1}, {1, 327, 2372, 2372, 327, 1}, {1, 1023, 15219, 34114, 15219, 1023, 1}, {1, 3145, 88839, 381775, 381775, 88839, 3145, 1}, {1, 9577, 490114, 3683815, 6934426, 3683815, 490114, 9577, 1}, {1, 29003, 2610590, 32334362, 103464764, 103464764, 32334362, 2610590, 29003, 1} MATHEMATICA Clear[p, x, n]; p[x_, n_] = (3*(x - 1)^(n)*Sum[(((-1)^(n)*(2*k + 1)^(n - 1)))*x^k, {k, 0, Infinity}] - (x - 1)^(n + 1)*Sum[((-1)^(n + 1)*k^n)*x^k, {k, 0, Infinity}]/x)/2; Table[FullSimplify[ExpandAll[p[x, n]]], {n, 1, 10}]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 1, 10}]; Flatten[%] CROSSREFS Sequence in context: A168517 A142465 A248829 * A033933 A108267 A156916 Adjacent sequences:  A154334 A154335 A154336 * A154338 A154339 A154340 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Jan 07 2009 STATUS approved

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Last modified October 22 00:52 EDT 2019. Contains 328315 sequences. (Running on oeis4.)