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a(n) = A356500(2*n+1, 2*n) for n >= 0.
3

%I #6 Aug 10 2022 07:56:48

%S 1,6,135,4284,160965,6684744,296679006,13805453160,665611197093,

%T 32988925715610,1671463040525586,86231285273788180,

%U 4516133521439246825,239551205985729110664,12846081444122599438850,695428535332816056597520,37960416340437631597631877

%N a(n) = A356500(2*n+1, 2*n) 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(2*n+1, 2*n),", "))

%Y Cf. A356500, A356504, A356506.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 09 2022