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Search: id:A089462
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| 1, 3, 14, 93, 822, 9193, 125292, 2022555, 37829468, 805712859, 19270873704, 511742870653, 14946235170120, 476314240239633, 16451368229689808, 612254102183085627, 24428043107239133712, 1040281158638494489075
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OFFSET
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0,2
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COMMENT
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A001858 enumerates forests of labeled trees with n nodes, and shifts 1 place left under the hyperbinomial transform.
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FORMULA
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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!).
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PROGRAM
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(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!))
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CROSSREFS
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Cf. A001858, A089460.
Sequence in context: A125788 A101220 A078456 this_sequence A088342 A074531 A091906
Adjacent sequences: A089459 A089460 A089461 this_sequence A089463 A089464 A089465
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 05 2003
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