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A089462 2nd hyperbinomial transform of A001858. 4
1, 3, 14, 93, 822, 9193, 125292, 2022555, 37829468, 805712859, 19270873704, 511742870653, 14946235170120, 476314240239633, 16451368229689808, 612254102183085627, 24428043107239133712, 1040281158638494489075 (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} 2*(n-k+2)^(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+2)^(n-m-j+1)*(m+j)!/(-2)^j)/m!.

MATHEMATICA

Table[Sum[Sum[Binomial[m, j]*Binomial[n, n - m - j + 1]*(n + 2)^(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+2)^(n-m-j+1)*(m+j)!/(-2)^j)/m!))

CROSSREFS

Cf. A001858, A089460.

Sequence in context: A101220 A078456 A195134 * A088342 A074531 A091906

Adjacent sequences:  A089459 A089460 A089461 * A089463 A089464 A089465

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 05 2003

STATUS

approved

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Last modified February 23 11:33 EST 2018. Contains 299579 sequences. (Running on oeis4.)