A352044 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * a(k).

1, 1, 1, 2, 4, 8, 16, 33, 71, 159, 367, 864, 2058, 4934, 11870, 28608, 69020, 166652, 402748, 974464, 2361416, 5733656, 13954488, 34054016, 83351472, 204659440, 504162416, 1246065920, 3089752480, 7685498976, 19174255584, 47971104769, 120326714335

Offset: 0

Author

Ilya Gutkovskiy, Mar 01 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A027826, A352045, A352066.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 2 k] a[k], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 32}]
nmax = 32; A[] = 0; Do[A[x] = 1 + x A[x^2/(1 - x)^2]/(1 - x) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

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

E.g.f.: Integral exp(x) * Sum_{n>=0} a(n) * x^(2*n) / (2*n)! dx.