A259205 E.g.f.: Sum_{n>=0} x^n * (2 + x^n)^n * exp(3*x^(n+1)) / n!.

1, 5, 15, 71, 217, 2075, 5833, 98075, 604897, 4102595, 69158473, 792527675, 2734836337, 113904191315, 1730614960633, 12894617703275, 210120481640257, 4657547039287235, 110056200990831433, 1516028212268193755, 8772198010091864977, 443429758927503346355, 18611452651483538546713

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(2*x^(n+1)) / n!.

Example

E.g.f.: A(x) = 1 + 5*x + 15*x^2/2! + 71*x^3/3! + 217*x^4/4! + 2075*x^5/5! +...
where
A(x) = exp(3*x) + x*(2+x)*exp(3*x^2) + x^2*(2+x^2)^2*exp(3*x^3)/2! + x^3*(2+x^3)^3*exp(3*x^4)/3! + x^4*(2+x^4)^4*exp(3*x^5)/4! + x^5*(2+x^5)^5*exp(3*x^6)/5! +...
also
A(x) = exp(2*x) + x*(3+x)*exp(2*x^2) + x^2*(3+x^2)^2*exp(2*x^3)/2! + x^3*(3+x^3)^3*exp(2*x^4)/3! + x^4*(3+x^4)^4*exp(2*x^5)/4! + x^5*(3+x^5)^5*exp(2*x^6)/5! +...

Prog

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

Crossrefs

Cf. A259202, A259203, A259204.

Sequence in context: A353173 A355603 A355507 * A149641 A149642 A149643

Adjacent sequences: A259202 A259203 A259204 * A259206 A259207 A259208

Keyword

nonn

Author

Paul D. Hanna, Jun 20 2015

Status

approved