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 A351057 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 6*x)) / (1 - 6*x). 4
 1, 1, 1, 7, 49, 349, 2593, 20755, 184609, 1851289, 20735041, 253471039, 3310505425, 45630322741, 660993079393, 10065000586507, 161262522401089, 2717539655666353, 48053169836707969, 888408313419305719, 17108882037936283249, 342144175940842590349, 7089944927940141776545 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Shifts 2 places left under 6th-order binomial transform. LINKS Table of n, a(n) for n=0..22. FORMULA a(0) = a(1) = 1; a(n) = Sum_{k=0..n-2} binomial(n-2,k) * 6^k * a(n-k-2). MATHEMATICA 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] 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}] CROSSREFS Cf. A005012, A007472, A007476, A351049, A351050, A351056. Sequence in context: A033143 A024582 A024587 * A240721 A233658 A344270 Adjacent sequences: A351054 A351055 A351056 * A351058 A351059 A351060 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Jan 30 2022 STATUS approved

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Last modified June 10 14:12 EDT 2023. Contains 363205 sequences. (Running on oeis4.)