A089467 Hyperbinomial transform of A089466 and also the inverse hyperbinomial transform of A089468.

1, 2, 8, 52, 478, 5706, 83824, 1461944, 29510268, 676549450, 17361810016, 492999348348, 15345359136232, 519525230896322, 19005788951346240, 747102849650454256, 31404054519248544016, 1405608808807797838866

Offset

0,2

Comments

See A088956 for the definition of the hyperbinomial transform.

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = sum(k=0, n, (n-k+1)^(n-k-1)*C(n, k)*A089466(k)). a(n) = sum(k=0, n, -(n-k-1)^(n-k-1)*C(n, k)*A089468(k)). a(n) = sum(m=0, n, sum(j=0, m, C(m, j)*C(n, n-m-j)*n^(n-m-j)*(m+j)!/(-2)^j)/m!)).

a(n) ~ exp(1/2) * n^n. - Vaclav Kotesovec, Oct 11 2020

Mathematica

Flatten[{1, Table[Sum[Sum[Binomial[m, j] * Binomial[n, n-m-j] * n^(n-m-j) * (m+j)! / (-2)^j / m!, {j, 0, m}], {m, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 11 2020 *)

Prog

(PARI) a(n)=if(n<0, 0, sum(m=0, n, sum(j=0, m, binomial(m, j)*binomial(n, n-m-j)*n^(n-m-j)*(m+j)!/(-2)^j)/m!))

Crossrefs

Cf. A089466, A089468, A088956.

Sequence in context: A006351 A300697 A277499 * A195192 A103239 A375904

Adjacent sequences: A089464 A089465 A089466 * A089468 A089469 A089470

Keyword

nonn

Author

Paul D. Hanna, Nov 08 2003

Status

approved