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%I #6 Feb 01 2022 19:59:19
%S 1,1,1,6,36,221,1431,10121,80311,718106,7111976,76201501,868288401,
%T 10438492181,132166853861,1763179150946,24776241643056,
%U 365971430085021,5662954240306111,91450179009971181,1536249848608545451,26782376261726525126,483792982362049317676
%N G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 5*x)) / (1 - 5*x).
%C Shifts 2 places left under 5th-order binomial transform.
%F a(0) = a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 5^k * a(n-k-2).
%t nmax = 22; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 - 5 x)]/(1 - 5 x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n - 2, k] 5^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 22}]
%Y Cf. A005011, A007472, A007476, A351049, A351050, A351057.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Jan 30 2022
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