cp's OEIS Frontend

A248615 E.g.f.: Sum_{n>=0} x^n * (1 + exp(n*x))^n.

%I A248615 #19 Nov 05 2014 04:55:47
%S A248615 1,2,10,99,1540,33765,978486,35904463,1617090728,87295834665,
%T A248615 5543664590890,407913496939971,34345772643864540,3274503583293002749,
%U A248615 350340544319075248862,41739496421354682909015,5500282856601438305701456,796938625536899521586167377,126293050155194034442298968914
%N A248615 E.g.f.: Sum_{n>=0} x^n * (1 + exp(n*x))^n.
%H A248615 Vaclav Kotesovec, <a href="/A248615/b248615.txt">Table of n, a(n) for n = 0..260</a>
%F A248615 E.g.f.: Sum_{n>=0} x^n * exp(n^2*x) / (1 - x*exp(n*x))^(n+1).
%e A248615 E.g.f.: A(x) = 1 + 2*x + 10*x^2/2! + 99*x^3/3! + 1540*x^4/4! + 33765*x^5/5! +...
%e A248615 where the e.g.f. satisfies following series identity:
%e A248615 A(x) = 1 + x*(1+exp(x)) + x^2*(1+exp(2*x))^2 + x^3*(1+exp(3*x))^3 + x^4*(1+exp(4*x))^4 + x^5*(1+exp(5*x))^5 + x^6*(1+exp(6*x))^6 +...
%e A248615 A(x) = 1/(1-x) + x*exp(x)/(1-x*exp(x))^2 + x^2*exp(4*x)/(1-x*exp(2*x))^3 + x^3*exp(9*x)/(1-x*exp(3*x))^4 + x^4*exp(16*x)/(1-x*exp(4*x))^5 + x^5*exp(25*x)/(1-x*exp(5*x))^6 + x^6*exp(36*x)/(1-x*exp(6*x))^7 +...
%o A248615 (PARI) {a(n, t=1)=local(A=1+x); A=sum(k=0, n, x^k * (t + exp(k*x +x*O(x^n)) +x*O(x^n))^k); n!*polcoeff(A, n)}
%o A248615 for(n=0, 20, print1(a(n,1), ", "))
%o A248615 (PARI) {a(n, t=1)=local(A=1+x); A=sum(k=0, n, exp(k^2*x +x*O(x^n))*x^k/(1 - t*exp(k*x +x*O(x^n))*x )^(k+1) ); n!*polcoeff(A, n)}
%o A248615 for(n=0, 20, print1(a(n,1), ", "))
%Y A248615 Cf. A193421.
%K A248615 nonn
%O A248615 0,2
%A A248615 _Paul D. Hanna_, Oct 09 2014