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A048998 Triangle giving coefficients of (n+1)!*B_n(x), where B_n(x) is a Bernoulli polynomial. Rising powers of x. 10
1, -1, 2, 1, -6, 6, 0, 12, -36, 24, -4, 0, 120, -240, 120, 0, -120, 0, 1200, -1800, 720, 120, 0, -2520, 0, 12600, -15120, 5040, 0, 6720, 0, -47040, 0, 141120, -141120, 40320, -12096, 0, 241920, 0, -846720, 0, 1693440, -1451520, 362880 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

See A074909 for generators for the Bernoulli polynomials and connections to the beheaded Pascal triangle and reciprocals of the integers. - Tom Copeland, Nov 17 2014

REFERENCES

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, 5th ed., Section 9.62.

LINKS

T. D. Noe, Rows n=0..50 of triangle, flattened

Index entries for sequences related to Bernoulli numbers.

FORMULA

t*exp(x*t)/(exp(t)-1) = Sum_{n >= 0} B_n(x)*t^n/n!.

a(n,m) = [x^m]((n+1)!*B_n(x)), n>=0, m=0,...,n. - Wolfdieter Lang, Jun 21 2011

EXAMPLE

B_0(x)=1; B_1(x)=x-1/2; B_2(x)=x^2-x+1/6; B_3(x)=x^3-3*x^2/2+x/2; B_4(x)=x^4-2*x^3+x^2-1/30; ...

Triangle starts:

   1;

  -1,  2;

   1, -6,   6;

   0, 12, -36, 24;

  ...

MAPLE

A048998 := proc(n, k) coeftayl(bernoulli(n, x), x=0, k) ; (n+1)!*% ; end proc:

seq(seq(A048998(n, k), k=0..n), n=0..10) ; # R. J. Mathar, Jun 27 2011

MATHEMATICA

Flatten[Table[CoefficientList[(n + 1)! BernoulliB[n, x], x], {n, 0, 10}]] (* T. D. Noe, Jun 21 2011 *)

CROSSREFS

Cf. A048999, A074909.

Sequence in context: A095132 A028940 A218853 * A213615 A049019 A133314

Adjacent sequences:  A048995 A048996 A048997 * A048999 A049000 A049001

KEYWORD

sign,easy,nice,tabl

AUTHOR

N. J. A. Sloane

EXTENSIONS

Added 'Rising powers of x' in name - Wolfdieter Lang, Jun 21 2011

STATUS

approved

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Last modified February 21 20:03 EST 2019. Contains 320377 sequences. (Running on oeis4.)