cp's OEIS Frontend

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

%I A202516 #11 Aug 12 2025 12:20:44
%S A202516 1,5,97,14735,22208431,314664801905,41448076127290195,
%T A202516 50905029765702161210225,582983891132858366160979787245,
%U A202516 62080074367851800086180277369110042475,61205889017397342360456211893643596980919936577
%N A202516 G.f.: exp( Sum_{n>=1} (2^n + 3^n)^n * x^n/n ).
%C A202516 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.
%e A202516 G.f.: A(x) = 1 + 5*x + 97*x^2 + 14735*x^3 + 22208431*x^4 +...
%e A202516 where
%e A202516 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 +...
%e A202516 more explicitly,
%e A202516 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 +...
%o A202516 (PARI) {a(n)=polcoeff(exp(sum(m=1,n,(2^m+3^m)^m*x^m/m)+x*O(x^n)),n)}
%Y A202516 Cf. A155200, A155201, A155202, A202517, A326555.
%K A202516 nonn
%O A202516 0,2
%A A202516 _Paul D. Hanna_, Dec 20 2011