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A225604 G.f.: exp( Sum_{n>=1} A002426(n^2) * x^n/n ), where A002426 is the central trinomial coefficients.

%I A225604 #10 Jan 15 2025 19:42:53
%S A225604 1,1,10,1056,1300253,16436676927,2026538428535847,
%T A225604 2377041996570919354629,26137381916593225072659360863,
%U A225604 2668615348740645885804068311893052895,2513426521807431879643802805359800329740903335,21735453667359385540995804455408000917620356989063370267
%N A225604 G.f.: exp( Sum_{n>=1} A002426(n^2) * x^n/n ), where A002426 is the central trinomial coefficients.
%F A225604 Logarithmic derivative yields A225602.
%e A225604 G.f.: A(x) = A(x) = 1 + x + 10*x^2 + 1056*x^3 + 1300253*x^4 + 16436676927*x^5 +...
%e A225604 where
%e A225604 log(A(x)) = x + 19*x^2/2 + 3139*x^3/3 + 5196627*x^4/4 + 82176836301*x^5/5 +...+ A225602(n)*x^n/n +...
%o A225604 (PARI) {A002426(n)=sum(k=0,n, binomial(n, k)*binomial(k, n-k))}
%o A225604 {a(n)=polcoeff(exp(sum(m=1,n+1,A002426(m^2)*x^m/m) +x*O(x^n)),n)}
%o A225604 for(n=0,20,print1(a(n),", "))
%Y A225604 Cf. A225602, A002426.
%K A225604 nonn
%O A225604 0,3
%A A225604 _Paul D. Hanna_, Aug 03 2013