A174494
a(n) = coefficient of x^n/(n-1)! in the 4-fold iteration of x*exp(x).
Original entry on oeis.org
1, 4, 28, 274, 3400, 50734, 880312, 17357736, 382463824, 9298086490, 246914949376, 7104423326356, 220000621675912, 7290852811359654, 257332393857067720, 9632914084301343304, 381050245422453157408
Offset: 1
E.g.f.: x + 4*x^2 + 28*x^3/2! + 274*x^4/3! + 3400*x^5/4! +...
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{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)}
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{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))))}
A174495
a(n) = coefficient of x^n/(n-1)! in the 5-fold iteration of x*exp(x).
Original entry on oeis.org
1, 5, 45, 575, 9425, 187455, 4367245, 116322645, 3479863345, 115353325835, 4192244804645, 165607074622665, 7060695856372105, 322973775761169135, 15770136907303728205, 818373668098974428885, 44963322539225628107105
Offset: 1
E.g.f.: x + 5*x^2 + 45*x^3/2! + 575*x^4/3! + 9425*x^5/4! +...
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{a(n)=local(F=x, xEx=x*exp(x+x*O(x^n))); for(i=1,5,F=subst(F, x, xEx));(n-1)!*polcoeff(F, n)}
A174496
a(n) = coefficient of x^n/(n-1)! in the 6-fold iteration of x*exp(x).
Original entry on oeis.org
1, 6, 66, 1041, 21216, 527631, 15441636, 518651881, 19630068656, 825581830491, 38159948599956, 1921319136589221, 104603652465885096, 6120324106269585751, 382829011514506048556, 25484466375276284094561
Offset: 1
E.g.f.: x + 6*x^2 + 66*x^3/2! + 1041*x^4/3! + 21216*x^5/4! +...
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{a(n)=local(F=x, xEx=x*exp(x+x*O(x^n))); for(i=1,6,F=subst(F, x, xEx));(n-1)!*polcoeff(F, n)}