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%I #7 Apr 20 2019 09:12:31
%S 1,4,76,6660,1214148,360017028,155971158524,92792475869316,
%T 72662261401182820,72535277610275191076,89993707128790337826108,
%U 135923590258991068525838404,245645913626844106827612648116,523530365452078270295671790495780,1299582478160711096602245632490049676,3717486179387360228033345648745010216196,12140428019954179186668584893988648261704852
%N G.f. A(x) satisfies: 1 = Sum_{n>=0} (1 + x)^(n*(n+1)*(n+2)/3!) / A(x)^n * 1/2^(n+1).
%H Paul D. Hanna, <a href="/A325214/b325214.txt">Table of n, a(n) for n = 0..50</a>
%F G.f. A(x) satisfies:
%F (1) 1 = Sum_{n>=0} (1 + x)^(n*(n+1)*(n+2)/3!) / A(x)^n * 1/2^(n+1).
%F (2) 1 = Sum_{n>=0} (1 + x)^((n+1)*(n+2)*(n+3)/3!) / A(x)^(n+1) * 1/2^(n+1).
%e G.f.: A(x) = 1 + 4*x + 76*x^2 + 6660*x^3 + 1214148*x^4 + 360017028*x^5 + 155971158524*x^6 + 92792475869316*x^7 + 72662261401182820*x^8 + ...
%e such that
%e 1 = 1/2 + (1+x)/(2^2*A(x)) + (1+x)^4/(2^3*A(x)^2) + (1+x)^10/(2^4*A(x)^3) + (1+x)^20/(2^5*A(x)^3) + (1+x)^35/(2^6*A(x)^5) + (1+x)^56/(2^7*A(x)^6) + ...
%e also,
%e 1 = (1+x)/(2*A(x)) + (1+x)^4/(2*A(x))^2 + (1+x)^10/(2*A(x))^3 + (1+x)^20/(2*A(x))^4 + (1+x)^35/(2*A(x))^5 + (1+x)^56/(2*A(x))^6 + ...
%o (PARI) /* Requires suitable precision */
%o {a(n) = my(A=[1]); for(i=0,n,
%o A=concat(A,0); A[#A] = round( polcoeff( sum(n=0,30*#A+100,(1+x +x*O(x^#A))^(n*(n+1)*(n+2)/3!) / Ser(A)^(n) * 1/2^(n+1)*1.),#A-1)););A[n+1]}
%o for(n=0,20,print1(a(n),", "))
%K nonn
%O 0,2
%A _Paul D. Hanna_, Apr 19 2019
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