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%I #5 Feb 01 2022 19:57:27
%S 1,1,1,7,49,349,2593,20755,184609,1851289,20735041,253471039,
%T 3310505425,45630322741,660993079393,10065000586507,161262522401089,
%U 2717539655666353,48053169836707969,888408313419305719,17108882037936283249,342144175940842590349,7089944927940141776545
%N G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 6*x)) / (1 - 6*x).
%C Shifts 2 places left under 6th-order binomial transform.
%F a(0) = a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 6^k * a(n-k-2).
%t nmax = 22; A[_] = 0; Do[A[x_] = 1 + x + x^2 A[x/(1 - 6 x)]/(1 - 6 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] 6^k a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 22}]
%Y Cf. A005012, A007472, A007476, A351049, A351050, A351056.
%K nonn
%O 0,4
%A _Ilya Gutkovskiy_, Jan 30 2022
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