A344489 a(n) = 1 + Sum_{k=0..n-2} binomial(n-1,k) * a(k).

1, 1, 2, 4, 11, 34, 122, 487, 2144, 10276, 53165, 294760, 1740950, 10899841, 72033470, 500664496, 3648211139, 27792215302, 220802394110, 1825428024367, 15672798590804, 139499676115312, 1285109772354941, 12235037442987028, 120220980122266010, 1217655627762149857

Offset: 0

Author

Ilya Gutkovskiy, May 21 2021

Keywords

• nonn

Crossrefs

Cf. A000296, A000629, A007476, A186021, A337186, A344490, A344491, A344492, A344493.

Programs

Mathematica

a[n_] := a[n] = 1 + Sum[Binomial[n - 1, k] a[k] , {k, 0, n - 2}]; Table[a[n], {n, 0, 25}]
nmax = 25; A[] = 0; Do[A[x] = (1 + x A[x/(1 - x)])/(1 - x^2) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

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