A259204 E.g.f.: Sum_{n>=0} x^n * (1 + x^n)^n * exp(4*x^(n+1)) / n!.

1, 5, 19, 89, 377, 2225, 10577, 93665, 663617, 5100545, 76194977, 612260225, 6223839617, 118553476865, 1339060610177, 13661081703425, 312123334199297, 3897935011677185, 87368492659073537, 1400293336853714945, 12252801722806859777, 556540136476601135105, 15342689556084969711617

Offset

0,2

Links

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

Formula

E.g.f.: Sum_{n>=0} x^n * (4 + x^n)^n * exp(x^(n+1)) / n!.

Example

 E.g.f.: A(x) = 1 + 5*x + 19*x^2/2! + 89*x^3/3! + 377*x^4/4! + 2225*x^5/5! +...
where
A(x) = exp(4*x) + x*(1+x)*exp(4*x^2) + x^2*(1+x^2)^2*exp(4*x^3)/2! + x^3*(1+x^3)^3*exp(4*x^4)/3! + x^4*(1+x^4)^4*exp(4*x^5)/4! + x^5*(1+x^5)^5*exp(4*x^6)/5! +...
also
A(x) = exp(x) + x*(4+x)*exp(x^2) + x^2*(4+x^2)^2*exp(x^3)/2! + x^3*(4+x^3)^3*exp(x^4)/3! + x^4*(4+x^4)^4*exp(x^5)/4! + x^5*(4+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(4*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!*(4 + 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, A259203, A259205.

Sequence in context: A149801 A149802 A149803 * A149804 A340994 A301702

Adjacent sequences: A259201 A259202 A259203 * A259205 A259206 A259207

Keyword

nonn

Author

Paul D. Hanna, Jun 20 2015

Status

approved