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A174493
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a(n) = coefficient of x^n/(n-1)! in the 3-fold iteration of x*exp(x).
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4
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1, 3, 15, 102, 861, 8598, 98547, 1270160, 18138601, 283754826, 4818884319, 88186786020, 1728395865021, 36091833338174, 799408841413051, 18708996086926272, 461095012437724881, 11931573394008790290
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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..18.
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FORMULA
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a(n) = Sum_{k=0..n, j=0..n-k} C(n,k)*C(n-k,j)*(k+1)^j*(k+1+j)^(n-k-j).
O.g.f.: Sum_{n>=1} A080108(n)*x^n/(1-n*x)^n, where A080108(n) = [x^n/(n-1)! ] E(E(x)) and E(x) = x*exp(x).
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EXAMPLE
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E.g.f.: x + 3*x^2 + 15*x^3/2! + 102*x^4/3! + 861*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, 3, 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*(k+1+j)^(n-1-k-j)))}
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CROSSREFS
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Cf. A174480, A080108, A174494, A174495, A174496.
Sequence in context: A348793 A135903 A185753 * A354122 A318618 A123184
Adjacent sequences: A174490 A174491 A174492 * A174494 A174495 A174496
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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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