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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

%I

%S 1,0,-1,0,-3,4,0,-1,4,-3,0,-15,140,-270,144,0,-1,20,-75,96,-40,0,-21,

%T 868,-5670,13104,-12600,4320,0,-1,84,-903,3360,-5600,4320,-1260,0,-15,

%U 2540,-43470,244944,-630000,820800,-529200,134400,0,-1,340,-9075,74592,-278040,544320,-582120,322560,-72576

%N A triangle whose rows add up to the numerators of the Bernoulli numbers. T(n, k) for n >= 0, 0 <= k <= n.

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

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

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

%e 1

%e 0, -1

%e 0, -3, 4

%e 0, -1, 4, -3

%e 0, -15, 140, -270, 144

%e 0, -1, 20, -75, 96, -40

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

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

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

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

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

%t 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 *)

%Y Cf. A027641, A131689, A141056, A325871.

%K sign,tabl

%O 0,5

%A _Peter Luschny_, Sep 17 2011

%E Edited by _Peter Luschny_, Jun 26 2019

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Last modified September 27 16:20 EDT 2020. Contains 337383 sequences. (Running on oeis4.)