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A089465
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3rd hyperbinomial transform of A001858; also the hyperbinomial transform of A089462.
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2
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1, 4, 23, 178, 1763, 21504, 313585, 5342068, 104376201, 2304582544, 56807530871, 1547599725720, 46202052688603, 1500629138909632, 52697989385197137, 1990117967149595824, 80440669725095395025, 3465573101368534916928
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A001858 enumerates forests of labeled trees with n nodes and shifts 1 place left under the hyperbinomial transform.
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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!).
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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!))
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CROSSREFS
| Cf. A001858, A089462, A089463.
Sequence in context: A025550 A067545 A004041 * A106174 A056814 A058863
Adjacent sequences: A089462 A089463 A089464 * A089466 A089467 A089468
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 05 2003
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