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A113662 G.f. satisfies: A(x) = (1 + x*(d/dx x*A(x)) )^2.

%I A113662 #22 Sep 16 2024 09:23:25
%S A113662 1,2,9,62,566,6372,84837,1300214,22511322,434226300,9231983850,
%T A113662 214481625516,5406323440492,146963638311880,4286068830850797,
%U A113662 133501081493969574,4423404073559930162,155359770700317171084
%N A113662 G.f. satisfies: A(x) = (1 + x*(d/dx x*A(x)) )^2.
%C A113662 Self-convolution of A000699 (after ignoring the initial term), [previous name].
%H A113662 Vaclav Kotesovec, <a href="/A113662/b113662.txt">Table of n, a(n) for n = 0..400</a>
%F A113662 G.f. satisfies: A(x) = (1 + x*(d/dx x*A(x)) )^2.
%F A113662 a(n) ~ 2^(n + 5/2) * n^(n+1) / exp(n+1). - _Vaclav Kotesovec_, Oct 23 2020
%e A113662 G.f. A(x) = 1 + 2*x + 9*x^2 + 62*x^3 + 566*x^4 + 6372*x^5 + 84837*x^6 + 1300214*x^7 + ...
%o A113662 (PARI) {a(n)=local(A=1+x*O(x^n));for(i=1,n, A=(1+x*deriv(x*A))^2);polcoeff(A,n,x)}
%o A113662 (PARI)
%o A113662 A000699_seq(N) = {
%o A113662   my(a = vector(N)); a[1] = 1;
%o A113662   for (n=2, N, a[n] = sum(k=1, n-1, (2*k-1)*a[k]*a[n-k])); a;
%o A113662 };
%o A113662 Vec(sqr(Ser(A000699_seq(N))))  \\ _Gheorghe Coserea_, Jan 23 2017
%Y A113662 Cf. A000699, A113663, A113664, A113665, A113666, A113667, A113668.
%K A113662 nonn
%O A113662 0,2
%A A113662 _Paul D. Hanna_, Nov 04 2005
%E A113662 Name replaced with an existing formula by _Paul D. Hanna_, Sep 16 2024