A351972 a(n) = 1 + Sum_{k=0..floor((n-1)/2)} a(k) * a(n-2*k-1).

1, 2, 3, 6, 11, 21, 40, 78, 151, 294, 572, 1115, 2172, 4234, 8252, 16088, 31361, 61140, 119191, 232370, 453010, 883167, 1721768, 3356675, 6543988, 12757830, 24871992, 48489172, 94531974, 184294706, 359291464, 700456240, 1365573493, 2662252082, 5190190005

Offset: 0

Author

Ilya Gutkovskiy, Feb 26 2022

Keywords

• nonn

Crossrefs

Cf. A000621, A007317, A351973.

Programs

Mathematica

a[n_] := a[n] = 1 + Sum[a[k] a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 34}]
nmax = 34; A[] = 0; Do[A[x] = 1/((1 - x) (1 - x A[x^2])) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

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