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%I #5 Apr 07 2022 12:10:20
%S 1,2,3,4,7,18,49,120,264,544,1100,2256,4736,10080,21456,45312,94850,
%T 197412,410134,852968,1778382,3719364,7806338,16451280,34835184,
%U 74164800,158854536,342478432,743432288,1625079936,3576582592,7922065408,17648409603
%N a(0) = 1; a(n) = Sum_{k=0..floor(n/4)} binomial(n+1,4*k+1) * a(k).
%C Self-convolution of A351971.
%F G.f. A(x) satisfies: A(x) = A(x^4/(1 - x)^4) / (1 - x)^2.
%F E.g.f.: d/dx ( exp(x) * Sum_{n>=0} a(n) * x^(4*n+1) / (4*n+1)! ).
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n + 1, 4 k + 1] a[k], {k, 0, Floor[n/4]}]; Table[a[n], {n, 0, 32}]
%t nmax = 32; A[_] = 1; Do[A[x_] = A[x^4/(1 - x)^4]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%Y Cf. A040027, A051163, A351971, A352901.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Apr 07 2022