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A174494 a(n) = coefficient of x^n/(n-1)! in the 4-fold iteration of x*exp(x). 4

%I #2 Mar 30 2012 18:37:21

%S 1,4,28,274,3400,50734,880312,17357736,382463824,9298086490,

%T 246914949376,7104423326356,220000621675912,7290852811359654,

%U 257332393857067720,9632914084301343304,381050245422453157408

%N a(n) = coefficient of x^n/(n-1)! in the 4-fold iteration of x*exp(x).

%F 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).

%F 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).

%F E.g.f. equals the 2-fold iteration of the e.g.f. of A080108.

%e E.g.f.: x + 4*x^2 + 28*x^3/2! + 274*x^4/3! + 3400*x^5/4! +...

%o (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)}

%o (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))))}

%Y Cf. A174480, A080108, A174493, A174495, A174496.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Apr 17 2010

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Last modified June 10 13:14 EDT 2023. Contains 363205 sequences. (Running on oeis4.)