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A089467
Hyperbinomial transform of A089466 and also the inverse hyperbinomial transform of A089468.
3
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.
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 08 2003
STATUS
approved