cp's OEIS Frontend

A112915 Recurrence: a(n) = Sum_{k=0..n-1} (k+1)*(n-k)*a(k)*a(n-k-1) for n>0, with a(0)=1.

%I A112915 #8 Aug 24 2017 05:38:59
%S A112915 1,1,4,28,272,3312,47872,794880,14840064,306900736,6953989120,
%T A112915 171200048128,4548965384192,129742326218752,3953689388187648,
%U A112915 128215703582343168,4409347536459988992,160304460015345795072
%N A112915 Recurrence: a(n) = Sum_{k=0..n-1} (k+1)*(n-k)*a(k)*a(n-k-1) for n>0, with a(0)=1.
%H A112915 Vaclav Kotesovec, <a href="/A112915/b112915.txt">Table of n, a(n) for n = 0..400</a>
%F A112915 A(x) = 1 + x*G(2*x)^2, where G(x) = g.f. of A088716, such that a(n) = 2^n*A088716(n)/(n+1) for n>=0.
%F A112915 a(n) = 2^(n-1)*A112916(n-1) for n>0.
%F A112915 G.f. satisfies: A(x) = 1 + x*(d/dx[x*A(x)])^2 = 1 + x*(A(x) + x*A'(x))^2.
%F A112915 a(n) ~ c * n * 2^n * n!, where c = A238223 = 0.21795078944715106549... - _Vaclav Kotesovec_, Aug 24 2017
%o A112915 (PARI) a(n)=if(n==0,1,sum(k=0,n-1,(k+1)*(n-k)*a(k)*a(n-k-1)))
%o A112915 (PARI) {a(n)=local(F=1+x+x*O(x^n));for(i=1,n,F=1+x*deriv(x*F)^2); return(polcoeff(F,n,x))}
%Y A112915 Cf. A088716, A112916, A238223.
%K A112915 nonn
%O A112915 0,3
%A A112915 _Paul D. Hanna_, Oct 06 2005