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A176665 A triangle of polynomial coefficients:p(x,n)=Sum[(k + 1)^n*k!*Binomial[x, k], {k, 0, n}] 0
1, 1, 2, 1, -5, 9, 1, 109, -165, 64, 1, -3303, 6188, -3494, 625, 1, 169711, -357254, 254434, -74635, 7776, 1, -13084359, 30063342, -24927719, 9549230, -1718079, 117649, 1, 1417404703, -3486909736, 3229823067, -1474126800, 354928391 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums are:A083318;

{1, 3, 5, 9, 17, 33, 65, 129, 257, 513, 1025,...}.

LINKS

Table of n, a(n) for n=0..33.

FORMULA

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

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

EXAMPLE

{1},

{1, 2},

{1, -5, 9},

{1, 109, -165, 64},

{1, -3303, 6188, -3494, 625},

{1, 169711, -357254, 254434, -74635, 7776},

{1, -13084359, 30063342, -24927719, 9549230, -1718079, 117649},

{1, 1417404703, -3486909736, 3229823067, -1474126800, 354928391, -43216649, 2097152},

{1, -205529562639, 534439222506, -539283913267, 279525603239, -81520352759, 13514487427, -1188530972, 43046721},

{1, 38459425717831, -104747375400796, 113245625429903, -64756869507279, 21712548717551, -4414028821223, 535286444036, -35612579511, 1000000000},

{1, -9025805440874919, 25574643294415530, -29279684023784495, 18120391694121439, -6767757249933644, 1596879145253140, -239745218700854, 22209046187271, -1157184107045, 25937424601}

MATHEMATICA

Clear[p, x, n]

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

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

Flatten[%]

CROSSREFS

Cf. A083318

Sequence in context: A222542 A318052 A026078 * A199050 A306539 A193629

Adjacent sequences:  A176662 A176663 A176664 * A176666 A176667 A176668

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Apr 23 2010

STATUS

approved

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Last modified April 19 02:51 EDT 2019. Contains 322237 sequences. (Running on oeis4.)