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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS See A088956 for the definition of the hyperbinomial transform. LINKS 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 A209307 Adjacent sequences:  A089464 A089465 A089466 * A089468 A089469 A089470 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 08 2003 STATUS approved

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Last modified August 3 17:21 EDT 2021. Contains 346439 sequences. (Running on oeis4.)