A202516 G.f.: exp( Sum_{n>=1} (2^n + 3^n)^n * x^n/n ).

1, 5, 97, 14735, 22208431, 314664801905, 41448076127290195, 50905029765702161210225, 582983891132858366160979787245, 62080074367851800086180277369110042475, 61205889017397342360456211893643596980919936577

Offset: 0

Author

Paul D. Hanna, Dec 20 2011

Keywords

• nonn

Comments

More generally, for integers p and q, exp( Sum_{n>=1} (p^n + q^n)^n * x^n/n ) is a power series in x with integer coefficients.

Examples

			G.f.: A(x) = 1 + 5*x + 97*x^2 + 14735*x^3 + 22208431*x^4 +...
where
log(A(x)) = (2+3)*x + (2^2 + 3^2)^2*x^2/2 + (2^3 + 3^3)^3*x^3/3 + (2^4 + 3^4)^4*x^4/4 + (2^5 + 3^5)^5*x^5/5 +...
more explicitly,
log(A(x)) = 5*x + 13^2*x^2/2 + 35^3*x^3/3 + 97^4*x^4/4 + 275^5*x^5/5 +...
		

Crossrefs

Cf. A155200, A155201, A155202, A202517, A326555.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1,n,(2^m+3^m)^m*x^m/m)+x*O(x^n)),n)}