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A143917 G.f. A(x) satisfies: A(x) = 1/(1-x) + x^2*A(x)*A'(x). 3

%I #17 Feb 12 2023 17:28:03

%S 1,1,2,6,25,133,851,6313,53061,497493,5144500,58161126,713789847,

%T 9453038227,134405493652,2042529150110,33045300698761,567165849906233,

%U 10294218618819268,197022941365579804,3966001076798967837

%N G.f. A(x) satisfies: A(x) = 1/(1-x) + x^2*A(x)*A'(x).

%H Vincenzo Librandi, <a href="/A143917/b143917.txt">Table of n, a(n) for n = 0..200</a>

%F a(n) ~ c * n!, where c = 1.81857005675331400362707139219522893237... (see A238214). - _Vaclav Kotesovec_, Feb 20 2014

%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 25*x^4 + 133*x^5 + 851*x^6 +...

%e A'(x) = 1 + 4*x + 18*x^2 + 100*x^3 + 665*x^4 + 5106*x^5 +...

%e A(x)*A'(x) = 1 + 5*x + 24*x^2 + 132*x^3 + 850*x^4 + 6312*x^5 +...

%t Clear[a]; a[0] = 1; a[n_]/; n>=1 := a[n] = 1 + Sum[(k - 1) a[k - 1] a[n - k], {k, n}]; Table[a[n], {n,0, 16}] (* _David Callan_, Jun 24 2013 *)

%o (PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x+x*O(x^n))+x^2*A*deriv(A)); polcoeff(A, n)}

%Y Cf. A143916 (variant), A238214.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 05 2008

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)