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%I #5 Jan 24 2018 18:42:43
%S 1,1,1,2,3,7,16,48,157,586,2362,10214,46672,223752,1118799,5810185,
%T 31237145,173412537,992006284,5837461604,35283954583,218791917313,
%U 1390314155401,9044905749879,60190822583318,409404760891303,2844213921090065,20168470493811065,145888129690256442,1075859539461621404,8084389249391405645,61869341164985700882,481984158600673224200
%N G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n / (1-x)^( n*(n+1) ) / A(x)^( (n+1)*(n+2)/2 ).
%H Paul D. Hanna, <a href="/A296231/b296231.txt">Table of n, a(n) for n = 0..200</a>
%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 7*x^5 + 16*x^6 + 48*x^7 + 157*x^8 + 586*x^9 + 2362*x^10 + 10214*x^11 + 46672*x^12 + 223752*x^13+ 1118799*x^14 + 5810185*x^15 + ...
%e such that
%e 1 = 1/A(x) + x/(1-x)^2/A(x)^3 + x^2/(1-x)^6/A(x)^6 + x^3/(1-x)^12/A(x)^10 + x^4/(1-x)^20/A(x)^15 + x^5/(1-x)^30/A(x)^21 + x^6/(1-x)^42/A(x)^28 + x^7/(1-x)^56/A(x)^36 + ...
%o (PARI) {a(n) = my(A=[1],V); for(i=0,n, A = concat(A,0); V = Vec(sum(n=0,#A,1/(1-x +x*O(x^#A))^(n*(n+1))*x^n/Ser(A)^((n+1)*(n+2)/2)) ); A[#A]=V[#A] ); A[n+1]}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A296230.
%K nonn
%O 0,4
%A _Paul D. Hanna_, Jan 24 2018
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