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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

Table of n, a(n) for n=0..39.

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: A071211 A222029 A038675 * A048159 A123527 A096611

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 November 26 16:10 EST 2014. Contains 250079 sequences.