A259203 E.g.f.: Sum_{n>=0} x^n * (1 + x^n)^n * exp(3*x^(n+1)) / n!.

1, 4, 12, 46, 178, 964, 4690, 42508, 285442, 2015524, 34230250, 201756988, 2251838962, 46808034004, 448004334970, 4600225964908, 96261481920322, 1498439279348164, 31186483536041290, 347205448551061468, 3507621455861824402, 206046694871148634804, 4533026667477585987610

Offset

0,2

Links

Table of n, a(n) for n=0..22.

Formula

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

Example

E.g.f.: A(x) = 1 + 4*x + 12*x^2/2! + 46*x^3/3! + 178*x^4/4! + 964*x^5/5! +...
where
A(x) = exp(3*x) + x*(1+x)*exp(3*x^2) + x^2*(1+x^2)^2*exp(3*x^3)/2! + x^3*(1+x^3)^3*exp(3*x^4)/3! + x^4*(1+x^4)^4*exp(3*x^5)/4! + x^5*(1+x^5)^5*exp(3*x^6)/5! +...
also
A(x) = exp(x) + x*(3+x)*exp(x^2) + x^2*(3+x^2)^2*exp(x^3)/2! + x^3*(3+x^3)^3*exp(x^4)/3! + x^4*(3+x^4)^4*exp(x^5)/4! + x^5*(3+x^5)^5*exp(x^6)/5! +...

Prog

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

Crossrefs

Cf. A259202, A259204, A259205.

Sequence in context: A149372 A126202 A149373 * A151464 A101225 A000775

Adjacent sequences: A259200 A259201 A259202 * A259204 A259205 A259206

Keyword

nonn

Author

Paul D. Hanna, Jun 20 2015

Status

approved