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A176666 A triangle of polynomial coefficients:p(x,n)=Sum[(2*k + 1)^n*k!*Binomial[x, k], {k, 0, n}] 0
1, 1, 3, 1, -16, 25, 1, 588, -904, 343, 1, -35108, 65593, -36965, 6561, 1, 3541662, -7450307, 5299298, -1551461, 161051, 1, -539667860, 1239476145, -1027098387, 393094596, -70630574, 4826809, 1, 115929493398, -285126982237, 264011385389 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums are:A103457;

{1, 4, 10, 28, 82, 244, 730, 2188, 6562, 19684, 59050,...}.

LINKS

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

FORMULA

p(x,n)=Sum[(2*k + 1)^n*k!*Binomial[x, k], {k, 0, n}];

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

EXAMPLE

{1},

{1, 3},

{1, -16, 25},

{1, 588, -904, 343},

{1, -35108, 65593, -36965, 6561},

{1, 3541662, -7450307, 5299298, -1551461, 161051},

{ 1, -539667860, 1239476145, -1027098387, 393094596, -70630574, 4826809},

{1, 115929493398, -285126982237, 264011385389, -120438105421, 28978650041, -3525298358, 170859375},

{1, -33405526460804, 86851508060145, -87619801707127, 45402414077950, -13236000326919, 2193188923598, -192758317723, 6975757441},

{1, 12439546100725062, -33876724511327305, 36619991865553925, -20936375400104384, 7018154767854372, -1426322806941012, 172905465804793, -11498169243547, 322687697779},

{1, -5815351979718349460, 16476663041157314889, -18861838035155184791, 11671607490973992658, -4358525114199083475, 1028212770824559839, -154333184246062051, 14292794059654483, -744463577761244, 16679880978201}

MATHEMATICA

Clear[p, x, n]

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

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

Flatten[%]

CROSSREFS

Cf. A103457

Sequence in context: A048159 A123527 A096611 * A162313 A188645 A060281

Adjacent sequences:  A176663 A176664 A176665 * A176667 A176668 A176669

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 23 2010

STATUS

approved

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Last modified December 20 23:03 EST 2014. Contains 252290 sequences.