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A174494
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a(n) = coefficient of x^n/(n-1)! in the 4-fold iteration of x*exp(x).
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4
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1, 4, 28, 274, 3400, 50734, 880312, 17357736, 382463824, 9298086490, 246914949376, 7104423326356, 220000621675912, 7290852811359654, 257332393857067720, 9632914084301343304, 381050245422453157408
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..17.
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FORMULA
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O.g.f.: Sum_{n>=1} A174493(n)*x^n/(1-n*x)^n, where A174493(n) = [x^n/(n-1)! ] E(E(E(x))) and E(x) = x*exp(x).
a(n)=Sum_{k=0..n-1, j=0..n-1-k, i=0..n-1-k-j} C(n-1,k)*C(n-1-k,j)*C(n-1-k-j,i)*(k+1)^j*(k+1+j)^i*(k+1+j+i)^(n-1-k-j-i).
E.g.f. equals the 2-fold iteration of the e.g.f. of A080108.
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EXAMPLE
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E.g.f.: x + 4*x^2 + 28*x^3/2! + 274*x^4/3! + 3400*x^5/4! +...
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PROG
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(PARI) {a(n)=local(F=x, xEx=x*exp(x+x*O(x^n))); for(i=1, 4, F=subst(F, x, xEx)); (n-1)!*polcoeff(F, n)}
(PARI) {a(n)=sum(k=0, n-1, binomial(n-1, k)*sum(j=0, n-1-k, binomial(n-1-k, j)*(k+1)^j*sum(i=0, n-1-k-j, binomial(n-1-k-j, i)*(k+1+j)^i*(k+1+j+i)^(n-1-k-j-i))))}
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CROSSREFS
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Cf. A174480, A080108, A174493, A174495, A174496.
Sequence in context: A302583 A302605 A303260 * A128318 A032274 A182964
Adjacent sequences: A174491 A174492 A174493 * A174495 A174496 A174497
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Apr 17 2010
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STATUS
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approved
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