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 A156653 Coefficients of a higher level infinite sum polynomial: p(x,n)=(1 - x)^(2n + 1)/((n + 1)*x^n)*Sum[(k + 1)^n*Binomial[k, n]*x^ k, {k, 0, Infinity}]. 0
 1, 1, 3, 1, 16, 13, 1, 125, 171, 39, 1, 1296, 2551, 1091, 101, 1, 16807, 43653, 28838, 5498, 243, 1, 262144, 850809, 780585, 243790, 24270, 561, 1, 4782969, 18689527, 22278189, 10073955, 1733035, 98661, 1263, 1, 100000000, 457947691, 677785807 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Roe sums are:A001761; {1, 1, 4, 30, 336, 5040, 95040, 2162160, 57657600, 1764322560, 60949324800,...}. LINKS FORMULA p(x,n)=(1 - x)^(2n + 1)/((n + 1)*x^n)*Sum[(k + 1)^n*Binomial[k, n]*x^ k, {k, 0, Infinity}]; t(n,m)=coefficients(p(x,n)). EXAMPLE {1}, {1}, {3, 1}, {16, 13, 1}, {125, 171, 39, 1}, {1296, 2551, 1091, 101, 1}, {16807, 43653, 28838, 5498, 243, 1}, {262144, 850809, 780585, 243790, 24270, 561, 1}, {4782969, 18689527, 22278189, 10073955, 1733035, 98661, 1263, 1}, {100000000, 457947691, 677785807, 410994583, 106215619, 10996369, 379693, 2797, 1}, {2357947691, 12400462713, 22055317500, 17027114412, 6066172434, 976428894, 64468572, 1406460, 6123, 1} MATHEMATICA Clear[p, x, n, m]; p[x_, n_] = (1 - x)^( 2n + 1)/((n + 1)*x^n)*Sum[(k + 1)^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], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A222029 A038675 A264902 * A048159 A276640 A123527 Adjacent sequences:  A156650 A156651 A156652 * A156654 A156655 A156656 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 12 2009 STATUS approved

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Last modified August 20 18:42 EDT 2017. Contains 290837 sequences.