A248654 E.g.f.: Sum_{n>=0} x^n * (3 + exp(n*x))^n.

1, 4, 34, 483, 10084, 286885, 10556406, 483876799, 26866889512, 1768601369961, 135698985275050, 11968589697570451, 1199598182911257372, 135313142875442335453, 17035239326998414091038, 2376497634554143028502855, 365070055205852728328220496, 61412309543674687202717299921

Offset: 0

Author

Paul D. Hanna, Oct 18 2014

Keywords

• nonn

Examples

			 G.f.: A(x) = 1 + 4*x + 34*x^2/2! + 483*x^3/3! + 10084*x^4/4! + 286885*x^5/5! +...
where the g.f. satisfies following series identity:
A(x) = 1 + x*(3+exp(x)) + x^2*(3+exp(2*x))^2 + x^3*(3+exp(3*x))^3 + x^4*(3+exp(4*x))^4 + x^5*(3+exp(5*x))^5 + x^6*(3+exp(6*x))^6 +...
A(x) = 1/(1-3*x) + x*exp(x)/(1-3*x*exp(x))^2 + x^2*exp(4*x)/(1-3*x*exp(2*x))^3 + x^3*exp(9*x)/(1-3*x*exp(3*x))^4 + x^4*exp(16*x)/(1-3*x*exp(4*x))^5 + x^5*exp(25*x)/(1-3*x*exp(5*x))^6 + x^6*exp(36*x)/(1-3*x*exp(6*x))^7 +...
		

Crossrefs

Cf. A248615, A248653, A193421.

Programs

PARI

{a(n,t=3)=local(A=1); A=sum(k=0, n, x^k * exp(k^2*x +x*O(x^n))/(1 - t*x*exp(k*x +x*O(x^n)))^(k+1) ); n!*polcoeff(A, n)}
for(n=0,25,print1(a(n,3),", "))

Formula

E.g.f.: Sum_{n>=0} x^n * exp(n^2*x)/(1 - 3*x*exp(n*x))^(n+1).