|
%I #9 Oct 08 2018 17:53:33
%S 1,1,2,37,1562313,122131737394518,26010968765974205465787541,
%T 22347536974721066092798325076069521074882,
%U 113454243067016764816945424312979214671918840299656114590507,897202601035299299315214220213621062686601174611936477408260666612934393100592315294994
%N G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^3, n^2*k) * x^k ).
%C Compare the definition to: exp( Sum_{n>=1} (1+y)^(n^3) * x^n/n ), which yields an integer series whenever y is an integer (e.g., A158110).
%C Note: exp( Sum_{n>=1} (1+x)^(n^3) * x^n/n ) does not yield an integer series.
%e G.f.: A(x) = 1 + x + 2*x^2 + 37*x^3 + 1562313*x^4 + 122131737394518*x^5 + ...
%e such that the logarithm equals
%e log(A(x)) = (1+x)*x + (1 + 70*x + x^2)*x^2/2
%e + (1 + 4686825*x + 4686825*x^2 + x^3)*x^3/3
%e + (1 + 488526937079580*x + 1832624140942590534*x^2 + 488526937079580*x^3 + x^4)*x^/4 + ...
%o (PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m^3, m^2*k)*x^k)*x^m/m)+x*O(x^n)), n)}
%o for(n=0, 15, print1(a(n), ", "))
%Y Cf. A158110, A206830, A227467.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Aug 24 2013
| 