A259202 E.g.f.: Sum_{n>=0} x^n * (1 + x^n)^n * exp(2*x^(n+1)) / n!.

1, 3, 7, 21, 89, 393, 2225, 18609, 101057, 816993, 13457825, 51228609, 810315137, 17176207233, 131372857985, 1305079808769, 26689011214337, 589160232591873, 8710689840914945, 54912598925708289, 1233406496755480577, 66645549104613373953, 1133684888589441378305, 7520981752666086084609, 200384978441063958102017

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

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

Example

E.g.f.: A(x) = 1 + 3*x + 7*x^2/2! + 21*x^3/3! + 89*x^4/4! + 393*x^5/5! +...
where
A(x) = exp(2*x) + x*(1+x)*exp(2*x^2) + x^2*(1+x^2)^2*exp(2*x^3)/2! + x^3*(1+x^3)^3*exp(2*x^4)/3! + x^4*(1+x^4)^4*exp(2*x^5)/4! + x^5*(1+x^5)^5*exp(2*x^6)/5! +...
also
A(x) = exp(x) + x*(2+x)*exp(x^2) + x^2*(2+x^2)^2*exp(x^3)/2! + x^3*(2+x^3)^3*exp(x^4)/3! + x^4*(2+x^4)^4*exp(x^5)/4! + x^5*(2+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(2*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!*(2 + 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. A259203, A259204, A259205.

Sequence in context: A049365 A288849 A031885 * A169981 A191294 A177820

Adjacent sequences: A259199 A259200 A259201 * A259203 A259204 A259205

Keyword

nonn

Author

Paul D. Hanna, Jun 20 2015

Status

approved