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A155868 A sequence of polynomial coefficients related to the first Stirling numbers: p(x,n)=If[n == 0, 1, 1 + x^n + Sum[(-1)^(n - 2*m)* StirlingS1[n, m]*StirlingS1[n, n - m]*x^m, {m, 0, n}]]. 0
1, 1, 1, 1, 1, 1, 1, 6, 6, 1, 1, 36, 121, 36, 1, 1, 240, 1750, 1750, 240, 1, 1, 1800, 23290, 50625, 23290, 1800, 1, 1, 15120, 308700, 1193640, 1193640, 308700, 15120, 1, 1, 141120, 4207896, 25738720, 45819361, 25738720, 4207896, 141120, 1, 1, 1451520 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are:

{1, 2, 3, 14, 195, 3982, 100807, 3034922, 105994835, 4215106730, 188097696347,...}

LINKS

Table of n, a(n) for n=0..46.

FORMULA

p(x,n)=If[n == 0, 1, 1 + x^n + Sum[(-1)^(n - 2*m)* StirlingS1[n, m]*StirlingS1[n, n - m]*x^m, {m, 0, n}]]

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

EXAMPLE

{1},

{1, 1},

{1, 1, 1},

{1, 6, 6, 1},

{1, 36, 121, 36, 1},

{1, 240, 1750, 1750, 240, 1},

{1, 1800, 23290, 50625, 23290, 1800, 1},

{1, 15120, 308700, 1193640, 1193640, 308700, 15120, 1},

{1, 141120, 4207896, 25738720, 45819361, 25738720, 4207896, 141120, 1},

{1, 1451520, 59832864, 535810464, 1510458516, 1510458516, 535810464, 59832864, 1451520, 1},

{1, 16329600, 893121120, 11082015000, 45789404640, 72535955625, 45789404640, 11082015000, 893121120, 16329600, 1}

MATHEMATICA

Clear[p, n, m, x, a];

p[x_, n_] = If[n == 0, 1, 1 + x^n + Sum[(-1)^(n - 2*m)* StirlingS1[n, m]*StirlingS1[n, n - m]*x^m, {m, 0, n}]];

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

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

Flatten[a]

CROSSREFS

Sequence in context: A046606 A172350 A205457 * A322622 A176565 A176567

Adjacent sequences:  A155865 A155866 A155867 * A155869 A155870 A155871

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Jan 29 2009

STATUS

approved

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Last modified April 5 17:03 EDT 2020. Contains 333245 sequences. (Running on oeis4.)