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a(n) = A356500(3*n, n+1) for n >= 0.
3

%I #5 Aug 10 2022 07:56:52

%S 1,6,120,3250,103020,3587696,133101836,5167564380,207615129579,

%T 8567305854998,361201849117032,15498967122249676,674906101555736960,

%U 29757755664623031984,1326196334421645347368,59655785739373960058296,2705420198806474232850741

%N a(n) = A356500(3*n, n+1) for n >= 0.

%C Triangle A356500 describes the coefficients in G(x,y) that satisfies: y = Sum_{n=-oo..+oo} (-x)^(n^2) * G(x,y)^((n-1)^2).

%o (PARI) {A356500(n,k) = my(A=[y],M); for(i=1,n, A = concat(A,0); M = ceil(sqrt(n+1));

%o A[#A] = -polcoeff( sum(m=-M,M, (-x)^(m^2)*Ser(A)^((m-1)^2)), #A-1)); polcoeff(A[n+1],k,y) }

%o for(n=0,20, print1( A356500(3*n, n+1),", "))

%Y Cf. A356500, A356504, A356505.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 09 2022