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A135743
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E.g.f.: A(x) = Sum_{n>=0} exp(n*(n+1)/2*x)*x^n/n!.
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5
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1, 1, 3, 13, 83, 686, 7132, 90343, 1357449, 23783068, 478784096, 10938189329, 280771780489, 8029138915630, 253911056912892, 8823070442039641, 335009138739028673, 13830540214264709000, 618085473234055115968
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = Sum_{k=0..n} C(n,k)*[k*(k+1)/2]^(n-k).
O.g.f.: Sum_{n>=0} x^n/(1 - n(n+1)/2*x)^(n+1).
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EXAMPLE
| E.g.f.: 1 + x + 3*x^2/2! + 13*x^3/3! + 83*x^4/4! +...
= 1 + exp(x)*x + exp(3x)*x^2/2! + exp(6x)*x^3/3! + exp(10x)*x^4/4! +...
O.g.f.: 1 + x + 3*x^2 + 13*x^3 + 83*x^4 + 686*x^5 +...
= 1 + x/(1-x)^2 + x^2/(1-3x)^3 + x^3/(1-6x)^4 + x^4/(1-10x)^5 +...
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PROG
| (PARI) {a(n)=sum(k=0, n, binomial(n, k)*(k*(k+1)/2)^(n-k))}
(PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(k*(k+1)/2*x +x*O(x^n))*x^k/k!), n)}
(PARI) {a(n)=polcoeff(sum(k=0, n, x^k/(1-k*(k+1)/2*x +x*O(x^n))^(k+1)), n)}
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CROSSREFS
| Cf. variants: A135742, A135744, A135745, A135746.
Sequence in context: A000904 A201304 A173998 * A123114 A104032 A130406
Adjacent sequences: A135740 A135741 A135742 * A135744 A135745 A135746
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 27 2007
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