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A100615 Let B(n)(x) be the Bernoulli polynomials as defined in A001898, with B(n)(1) equal to the usual Bernoulli numbers A027641/A027642. Sequence gives numerators of B(n)(2). 7
1, -1, 5, -1, 1, 1, -5, -1, 7, 3, -15, -5, 7601, 691, -91, -35, 3617, 3617, -745739, -43867, 3317609, 1222277, -5981591, -854513, 5436374093, 1181820455, -213827575, -76977927, 213745149261, 23749461029, -249859397004145, -8615841276005, 238988952277727, 84802531453387 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

F. N. David, Probability Theory for Statistical Methods, Cambridge, 1949; see pp. 103-104. [There is an error in the recurrence for B_s^{(r)}.]

LINKS

Robert Israel, Table of n, a(n) for n = 0..575

FORMULA

E.g.f.: (x/(exp(x)-1))^2. - Vladeta Jovovic, Feb 27 2006

a(n) = numerator(Sum_{k=0..n}(-1)^k*k!/(k+1)*Sum_{j=0..n-k} C(n,j)*Stirling2(n-j,k)*B(j)), where B(n) is Bernoulli numbers. - Vladimir Kruchinin, Jun 02 2015

EXAMPLE

1, -1, 5/6, -1/2, 1/10, 1/6, -5/42, -1/6, 7/30, 3/10, -15/22, -5/6, 7601/2730, 691/210, -91/6, -35/2, 3617/34, 3617/30, -745739/798, -43867/42, ... = A100615/A100616.

MAPLE

S:= series((x/(exp(x)-1))^2, x, 41):

seq(numer(coeff(S, x, j)*j!), j=0..40); # Robert Israel, Jun 02 2015

MATHEMATICA

Table[Numerator@NorlundB[n, 2], {n, 0, 32}] (* Arkadiusz Wesolowski, Oct 22 2012 *)

PROG

(Maxima)

a(n):=sum((-1)^k*k!/(k+1)*sum(binomial(n, j)*stirling2(n-j, k)*bern(j), j, 0, n-k), k, 0, n); /* Vladimir Kruchinin, Jun 02 2015 */

CROSSREFS

Cf. A001898, A027641, A027642, A100616.

Sequence in context: A066803 A089608 A250131 * A293897 A222119 A102280

Adjacent sequences:  A100612 A100613 A100614 * A100616 A100617 A100618

KEYWORD

sign,frac

AUTHOR

N. J. A. Sloane, Dec 03 2004

STATUS

approved

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Last modified April 19 21:09 EDT 2019. Contains 322291 sequences. (Running on oeis4.)