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A174859 A triangle sequence of polynomial coefficients:p(x,n)=Sum[Binomial[n, k]*(-x)^k*Sum[StirlingS2[n, m]*x^m, {m, 0, n - k}], {k, 0, n}] 0
1, 0, 1, 0, 1, -1, 0, 1, 0, -5, 0, 1, 3, -16, 15, 0, 1, 10, -40, 25, 56, 0, 1, 25, -81, -30, 370, -455, 0, 1, 56, -119, -469, 1841, -1960, -237, 0, 1, 119, -22, -2527, 7448, -5768, -7420, 16947, 0, 1, 246, 766, -10359, 24627, -2289, -76692, 126504, -64220, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

Row sums are:

{1, 1, 0, -4, 3, 52, -170, -887, 8778, -1416, -415734,...}.

REFERENCES

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 77.

LINKS

Table of n, a(n) for n=0..56.

FORMULA

p(x,n)=Sum[Binomial[n, k]*(-x)^k*Sum[StirlingS2[n, m]*x^m, {m, 0, n - k}], {k, 0, n}];

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

EXAMPLE

{1},

{0, 1},

{0, 1, -1},

{0, 1, 0, -5},

{0, 1, 3, -16, 15},

{0, 1, 10, -40, 25, 56},

{0, 1, 25, -81, -30, 370, -455},

{0, 1, 56, -119, -469, 1841, -1960, -237},

{0, 1, 119, -22, -2527, 7448, -5768, -7420, 16947},

{0, 1, 246, 766, -10359, 24627, -2289, -76692, 126504, -64220},

{0, 1, 501, 4265, -36320, 60215, 119760, -570627, 784245, -248280, -529494}

MATHEMATICA

Clear[p, x, n];

p[x_, n_] = Sum[Binomial[n, k]*(-x)^k*Sum[StirlingS2[n, m]*x^m, {m, 0, n - k}], {k, 0, n}];

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

Flatten[%]

CROSSREFS

Cf. A008299

Sequence in context: A117015 A325736 A334364 * A274619 A230844 A054672

Adjacent sequences:  A174856 A174857 A174858 * A174860 A174861 A174862

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Mar 31 2010

STATUS

approved

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Last modified January 26 05:13 EST 2022. Contains 350572 sequences. (Running on oeis4.)