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A134055
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a(n) = Sum_{k=0..n} C(n,k)*S2(n+1,k+1), where S2(n,k) = A048993(n,k) are Stirling numbers of the 2nd kind.
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0
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1, 2, 8, 41, 252, 1782, 14121, 123244, 1169832, 11960978, 130742196, 1518514076, 18645970943, 241030821566, 3268214127548, 46338504902485, 685145875623056, 10538790233183702, 168282662416550040, 2784205185437851772
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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EXAMPLE
| a(3) = 1*1 + 3*7 + 3*6 + 1*1 = 41;
a(4) = 1*1 + 4*15 + 6*25 + 4*10 + 1*1 = 252;
a(5) = 1*1 + 5*31 + 10*90 + 10*65 + 5*15 + 1*1 = 1782.
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PROG
| (PARI) {a(n)=sum(k=0, n, binomial(n, k)*polcoeff(1/prod(i=0, k+1, 1-i*x +x*O(x^(n-k))), n-k))}
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CROSSREFS
| Cf. A048993.
Sequence in context: A067119 A093935 A099240 * A136281 A125698 A052447
Adjacent sequences: A134052 A134053 A134054 * A134056 A134057 A134058
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Oct 08 2007
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