A344490 a(n) = 1 + Sum_{k=0..n-3} binomial(n-2,k) * a(k).

1, 1, 1, 2, 4, 8, 20, 57, 171, 548, 1894, 6998, 27368, 112653, 486645, 2201162, 10397944, 51161168, 261571460, 1386846249, 7612315023, 43190917004, 252951090586, 1527112817054, 9492126182336, 60677428545165, 398489257136529, 2686088269505042, 18567557376240748

Offset

0,4

Links

Table of n, a(n) for n=0..28.

Formula

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

Mathematica

a[n_] := a[n] = 1 + Sum[Binomial[n - 2, k] a[k] , {k, 0, n - 3}]; Table[a[n], {n, 0, 28}]
nmax = 28; A[_] = 0; Do[A[x_] = (1 + x^2 A[x/(1 - x)])/((1 - x) (1 + x^2)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A000629, A210540, A344489, A344491, A344492, A344493.

Sequence in context: A113180 A000116 A302862 * A006407 A100447 A241891

Adjacent sequences: A344487 A344488 A344489 * A344491 A344492 A344493

Keyword

nonn

Author

Ilya Gutkovskiy, May 21 2021

Status

approved