A332885 a(0) = a(1) = 1; a(n) = a(n-2) + Sum_{k=0..n-2} binomial(n-2,k) * a(k).

1, 1, 2, 3, 7, 16, 43, 123, 384, 1283, 4575, 17294, 69013, 289613, 1273934, 5856811, 28070535, 139936316, 724141487, 3882776711, 21536499372, 123388080843, 729195916303, 4439611287834, 27814781772073, 179132776279001, 1184720299683034, 8038979166269203

Offset

0,3

Links

Table of n, a(n) for n=0..27.

Formula

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

Mathematica

a[0] = a[1] = 1; a[n_] := a[n] = a[n - 2] + Sum[Binomial[n - 2, k] a[k], {k, 0, n - 2}]; Table[a[n], {n, 0, 27}]
nmax = 27; A[_] = 0; Do[A[x_] = 1 + x + x^2 (A[x] + (1/(1 - x)) A[x/(1 - x)]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A000110, A007476, A040027.

Sequence in context: A143884 A227546 A301902 * A122031 A246829 A296231

Adjacent sequences: A332882 A332883 A332884 * A332886 A332887 A332888

Keyword

nonn

Author

Ilya Gutkovskiy, Jul 04 2020

Status

approved