A351756 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - 2*x)) / (1 - 2*x)^2.

1, 1, 5, 23, 119, 709, 4749, 35031, 281271, 2438565, 22673021, 224739303, 2363075191, 26246762213, 306830932749, 3763323446487, 48292462190743, 646763208308421, 9020009372203965, 130737162573013159, 1965798562640921879, 30613694640191725381

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k-1) * 2^(k-1) * a(n-k).

Mathematica

nmax = 21; A[_] = 0; Do[A[x_] = 1 + x A[x/(1 - 2 x)]/(1 - 2 x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k - 1] 2^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]

Crossrefs

Cf. A004211, A040027, A122704, A351757.

Sequence in context: A193704 A294356 A162815 * A033312 A151881 A229811

Adjacent sequences: A351753 A351754 A351755 * A351757 A351758 A351759

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 18 2022

Status

approved