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A152924 A polynomial sum of two Stirling types: p(x,n)=(If[n == 0, 0, Sum[StirlingS2[ n, m]*x^m, {m, 0, n}]/x] + Sum[Abs[StirlingS1[n, m]]*x^m, {m, 0, n}]. 0
1, 1, 1, 1, 2, 1, 1, 5, 4, 1, 1, 13, 17, 7, 1, 1, 39, 75, 45, 11, 1, 1, 151, 364, 290, 100, 16, 1, 1, 783, 2065, 1974, 875, 196, 22, 1, 1, 5167, 14034, 14833, 7819, 2226, 350, 29, 1, 1, 40575, 112609, 125894, 74235, 25095, 4998, 582, 37, 1, 1, 363391, 1035906, 1206805 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are:

{1, 2, 4, 11, 39, 172, 923, 5917, 44460, 384027, 3744775,...}

LINKS

Table of n, a(n) for n=0..58.

FORMULA

p(x,n)=(If[n == 0, 0, Sum[StirlingS2[ n, m]*x^m, {m, 0, n}]/x] + Sum[Abs[StirlingS1[n, m]]*x^m, {m, 0, n}];

t*n,m)=Coefficients(p(x,m)).

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 5, 4, 1},

{1, 13, 17, 7, 1},

{1, 39, 75, 45, 11, 1},

{1, 151, 364, 290, 100, 16, 1},

{1, 783, 2065, 1974, 875, 196, 22, 1},

{1, 5167, 14034, 14833, 7819, 2226, 350, 29, 1},

{1, 40575, 112609, 125894, 74235, 25095, 4998, 582, 37, 1},

{1, 363391, 1035906, 1206805, 766205, 292152, 69153, 10200, 915, 46, 1}

MATHEMATICA

Clear[t, p, x, n];

p[x_, n_] = (If[n == 0, 0, Sum[StirlingS2[ n, m]*x^m, {m, 0, n}]/x] + Sum[Abs[StirlingS1[n, m]]*x^m, {m, 0, n}]);

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

Flatten[%]

CROSSREFS

Sequence in context: A263324 A284949 A241500 * A220738 A284732 A327483

Adjacent sequences:  A152921 A152922 A152923 * A152925 A152926 A152927

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Dec 15 2008

STATUS

approved

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Last modified October 23 19:26 EDT 2021. Contains 348215 sequences. (Running on oeis4.)