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%I #11 Apr 03 2016 02:10:37
%S 1,1,1,2,5,15,46,149,495,1682,5806,20322,71919,256936,925298,3355509,
%T 12242471,44906105,165503745,612575796,2276024836,8485972958,
%U 31739314999,119054638380,447759005393,1688108544222,6378722610280,24153083898505,91633201241544,348270745289976,1325907389447937,5055855150302197,19307179347881167,73832434701139921,282712142418209398,1083873025643898568,4160250292584533013,15986022831150313756,61491665982535018897
%N G.f. A(x) satisfies: 1/(1-x) = Product_{n>=1} A( x^n - x^(n+1) ).
%H Vaclav Kotesovec, <a href="/A268648/b268648.txt">Table of n, a(n) for n = 0..222</a>
%F a(n) ~ c * 4^n / n^(3/2), where c = 0.197157770057765155... . - _Vaclav Kotesovec_, Apr 02 2016
%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 15*x^5 + 46*x^6 + 149*x^7 + 495*x^8 + 1682*x^9 + 5806*x^10 + 20322*x^11 + 71919*x^12 +...
%e where
%e 1/(1-x) = A(x-x^2) * A(x^2-x^3) * A(x^3-x^4) * A(x^4-x^5) * A(x^5-x^6) *...
%e RELATED SERIES.
%e A(x-x^2) = 1 + x + x^5 - x^6 + 3*x^7 - 3*x^8 + 6*x^9 - 12*x^10 + 33*x^11 +...
%e A(x^2-x^3) = 1 + x^2 - x^3 + x^4 - 2*x^5 + 3*x^6 - 6*x^7 + 11*x^8 - 22*x^9 +...
%e A(x^3-x^4) = 1 + x^3 - x^4 + x^6 - 2*x^7 + x^8 + 2*x^9 - 6*x^10 + 6*x^11 +...
%e A(x^4-x^5) = 1 + x^4 - x^5 + x^8 - 2*x^9 + x^10 + 2*x^12 - 6*x^13 + 6*x^14 +...
%e ...
%o (PARI) {a(n) = my(A=[1,1]); for(i=1,n, A=concat(A,0); A[#A] = 1 - Vec( prod(k=1,#A, subst(Ser(A),x,x^k*(1-x))) )[#A] );A[n+1]}
%o for(n=0,40,print1(a(n),", "))
%K nonn
%O 0,4
%A _Paul D. Hanna_, Mar 26 2016
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