A218669 O.g.f.: Sum_{n>=0} 1/(1-n^3*x)^n * x^n/n! * exp(-x/(1-n^3*x)).

1, 0, 1, 7, 97, 1561, 41136, 1551814, 72440460, 4281320257, 324623105584, 30086950057627, 3299720918091511, 428431079916572044, 65637957066642609845, 11659659637028895337265, 2367270866164121777222596, 546795407830461739380895161, 143176487805296033192642234802

Offset: 0

Author

Paul D. Hanna, Nov 04 2012

Keywords

• nonn

Comments

Compare g.f. to the curious identity:

1/(1-x^2) = Sum_{n>=0} (1+n*x)^n * x^n/n! * exp(-x*(1+n*x)).

Examples

			O.g.f.: A(x) = 1 + x^2 + 7*x^3 + 97*x^4 + 1561*x^5 + 41136*x^6 +...
where
A(x) = exp(-x) + x/(1-x)*exp(-x/(1-x)) + x^2/(1-8*x)^2/2!*exp(-x/(1-8*x)) + x^3/(1-27*x)^3/3!*exp(-x/(1-27*x)) + x^4/(1-64*x)^4/4!*exp(-x/(1-64*x)) + x^5/(1-125*x)^5/5!*exp(-x/(1-125*x)) +...
simplifies to a power series in x with integer coefficients.
		

Crossrefs

Cf. A218667, A218668, A218670, A217900.

Programs

PARI

{a(n)=local(A=1+x,X=x+x*O(x^n));A=sum(k=0,n,1/(1-k^3*X)^k*x^k/k!*exp(-X/(1-k^3*X)));polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))