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A194587 A triangle whose rows add up to the numerators of the Bernoulli numbers. T(n, k) for n >= 0, 0 <= k <= n. 2
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, -278040, 544320, -582120, 322560, -72576 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..54.

FORMULA

T(n, k) = (-1)^k*A131689(n,k) * A141056(k)/(k+1).

Sum_{k=0..n} T(n,k) = A027641(n).

T(n, n) = (-1)^n*A325871(n).

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);

MATHEMATICA

T[n_, k_] := Times @@ Select[Divisors[n]+1, PrimeQ] (-1)^k StirlingS2[n, k]* k!/(k+1); Table[T[n, k], {n, 0, 9}, {k, 0, n}] (* Jean-Fran├žois Alcover, Jun 26 2019 *)

CROSSREFS

Cf. A027641, A131689, A141056, A325871.

Sequence in context: A107681 A021298 A170952 * A175646 A324362 A073234

Adjacent sequences:  A194584 A194585 A194586 * A194588 A194589 A194590

KEYWORD

sign,tabl

AUTHOR

Peter Luschny, Sep 17 2011

EXTENSIONS

Edited by Peter Luschny, Jun 26 2019

STATUS

approved

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Last modified August 9 03:35 EDT 2020. Contains 336319 sequences. (Running on oeis4.)