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A194587 Triangle read by rows, n>=0, 0<=k<=n, T(n,k) = (-1)^k*A131689(n,k) *A141056(k)/(k+1). 1
1, 0, -1, 0, -3, 4, 0, -1, 4, -3, 0, -15, 140, -270, 144, 0, -1, 20, -75, 96, -40, 0, -21, 868, -5670, 13104, -12600, 4320, 0, -1, 84, -903, 3360, -5600, 4320, -1260, 0, -15, 2540, -43470, 244944, -630000, 820800, -529200, 134400, 0, -1, 340, -9075, 74592 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Sum_{k=0..n} T(n,k) are the numerators of the Bernoulli numbers, A027641(n).

LINKS

Table of n, a(n) for n=0..49.

EXAMPLE

                    1

                  0, -1

                 0, -3, 4

               0, -1, 4, -3

          0, -15, 140, -270, 144

         0, -1, 20, -75, 96, -40

0, -21, 868, -5670, 13104, -12600, 4320

MAPLE

A194587 := proc(n, k) local i;

mul(i, i=select(isprime, map(i->i+1, numtheory[divisors](n)))):

(-1)^k*combinat[stirling2](n, k)*k!/(k+1): %%*% end:

seq(print(seq(A194587(n, k), k=0..n)), n=0..7);

CROSSREFS

Sequence in context: A107681 A021298 A170952 * A175646 A073234 A123685

Adjacent sequences:  A194584 A194585 A194586 * A194588 A194589 A194590

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Sep 17 2011

STATUS

approved

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Last modified February 21 10:49 EST 2019. Contains 320372 sequences. (Running on oeis4.)