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 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. 7
 1, 1, 4, 28, 272, 3312, 47872, 794880, 14840064, 306900736, 6953989120, 171200048128, 4548965384192, 129742326218752, 3953689388187648, 128215703582343168, 4409347536459988992, 160304460015345795072 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..400 FORMULA 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. a(n) = 2^(n-1)*A112916(n-1) for n>0. G.f. satisfies: A(x) = 1 + x*(d/dx[x*A(x)])^2 = 1 + x*(A(x) + x*A'(x))^2. a(n) ~ c * n * 2^n * n!, where c = A238223 = 0.21795078944715106549... - Vaclav Kotesovec, Aug 24 2017 PROG (PARI) a(n)=if(n==0, 1, sum(k=0, n-1, (k+1)*(n-k)*a(k)*a(n-k-1))) (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))} CROSSREFS Cf. A088716, A112916, A238223. Sequence in context: A245060 A191686 A231694 * A129683 A367474 A360730 Adjacent sequences: A112912 A112913 A112914 * A112916 A112917 A112918 KEYWORD nonn AUTHOR Paul D. Hanna, Oct 06 2005 STATUS approved

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Last modified September 12 17:41 EDT 2024. Contains 375853 sequences. (Running on oeis4.)