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A089465 3rd hyperbinomial transform of A001858; also the hyperbinomial transform of A089462. 3
1, 4, 23, 178, 1763, 21504, 313585, 5342068, 104376201, 2304582544, 56807530871, 1547599725720, 46202052688603, 1500629138909632, 52697989385197137, 1990117967149595824, 80440669725095395025, 3465573101368534916928 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A001858 enumerates forests of labeled trees with n nodes and shifts 1 place left under the hyperbinomial transform.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..385

FORMULA

a(n) = Sum_{k=0..n} 3*(n-k+3)^(n-k-1)*C(n, k)*A001858(k).

a(n) = Sum_{m=0..(n+1)} ( Sum_{j=0..m} C(m, j)*C(n, n-m-j+1)*(n+3)^(n-m-j+1)*(m+j)!/(-2)^j )/m!.

a(n) ~ 3 * exp(7/2) * n^(n-1). - Vaclav Kotesovec, Oct 11 2020

MATHEMATICA

Table[Sum[Sum[Binomial[m, j]*Binomial[n, n - m - j + 1]*(n + 3)^(n - m - j + 1)*(m + j)!/(-2)^j, {j, 0, m}]/m!, {m, 0, n + 1}], {n, 0, 50}] (* G. C. Greubel, Nov 18 2017 *)

PROG

(PARI) a(n)=if(n<0, 0, sum(m=0, n+1, sum(j=0, m, binomial(m, j)*binomial(n, n-m-j+1)*(n+3)^(n-m-j+1)*(m+j)!/(-2)^j)/m!))

CROSSREFS

Cf. A001858, A089462, A089463.

Sequence in context: A067545 A004041 A220353 * A220214 A106174 A056814

Adjacent sequences:  A089462 A089463 A089464 * A089466 A089467 A089468

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 05 2003

STATUS

approved

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Last modified June 23 05:11 EDT 2021. Contains 345395 sequences. (Running on oeis4.)