A351056 G.f. A(x) satisfies: A(x) = 1 + x + x^2 * A(x/(1 - 5*x)) / (1 - 5*x).

1, 1, 1, 6, 36, 221, 1431, 10121, 80311, 718106, 7111976, 76201501, 868288401, 10438492181, 132166853861, 1763179150946, 24776241643056, 365971430085021, 5662954240306111, 91450179009971181, 1536249848608545451, 26782376261726525126, 483792982362049317676

Offset

0,4

Comments

Shifts 2 places left under 5th-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) * 5^k * a(n-k-2).

Mathematica

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]
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}]

Crossrefs

Cf. A005011, A007472, A007476, A351049, A351050, A351057.

Sequence in context: A129324 A180218 A218991 * A166748 A200378 A085687

Adjacent sequences: A351053 A351054 A351055 * A351057 A351058 A351059

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 30 2022

Status

approved