A218668 O.g.f.: Sum_{n>=0} 1/(1-n^2*x)^n * x^n/n! * exp(-x/(1-n^2*x)).

1, 0, 1, 3, 22, 161, 1546, 18857, 270320, 4471693, 85455574, 1865128265, 45735737037, 1247518965519, 37654095184226, 1250673144714138, 45415758777730668, 1792734161930717221, 76595370803745016626, 3529261203030717032927, 174742139545017029583279

Offset

0,4

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)).

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..290

Example

O.g.f.: A(x) = 1 + x^2 + 3*x^3 + 22*x^4 + 161*x^5 + 1546*x^6 + 18857*x^7 +...
where
A(x) = exp(-x) + x/(1-x)*exp(-x/(1-x)) + x^2/(1-4*x)^2/2!*exp(-x/(1-4*x)) + x^3/(1-9*x)^3/3!*exp(-x/(1-9*x)) + x^4/(1-16*x)^4/4!*exp(-x/(1-16*x)) + x^5/(1-25*x)^5/5!*exp(-x/(1-25*x)) +...
simplifies to a power series in x with integer coefficients.

Prog

(PARI) {a(n)=local(A=1+x, X=x+x*O(x^n)); A=sum(k=0, n, 1/(1-k^2*X)^k*x^k/k!*exp(-X/(1-k^2*X))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A218667, A218669, A218670, A217900.

Sequence in context: A041661 A037586 A183259 * A164021 A192365 A074578

Adjacent sequences: A218665 A218666 A218667 * A218669 A218670 A218671

Keyword

nonn

Author

Paul D. Hanna, Nov 04 2012

Status

approved