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A178087 G.f. satisfies: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} A(k*x). 2

%I

%S 1,1,2,6,25,141,1071,11011,154739,3005187,81434048,3101253384,

%T 166823865867,12719913809811,1378095292930494,212524751143894194,

%U 46713381928627546015,14648866052370410611923,6558913185973371123604314,4195585528812861561212654010

%N G.f. satisfies: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} A(k*x).

%H Paul D. Hanna, <a href="/A178087/b178087.txt">Table of n, a(n) for n = 0..60</a>

%e G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 25*x^4 + 141*x^5 +...

%e where

%e A(x) = 1 + x*A(x) + x^2*A(x)*A(2*x) + x^3*A(x)*A(2*x)*A(3*x) + x^4*A(x)*A(2*x)*A(3*x)*A(4*x) + x^5*A(x)*A(2*x)*A(3*x)*A(4*x)*A(5*x) +...

%o (PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*prod(k=1, m, subst(A, x, k*x+x*O(x^n))))); polcoeff(A, n)}

%o for(n=0,20,print1(a(n),", "))

%Y Cf. A230317.

%K nonn

%O 0,3

%A _Paul D. Hanna_, May 19 2010

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Last modified July 1 07:30 EDT 2022. Contains 354952 sequences. (Running on oeis4.)