A346771 G.f. A(x) satisfies: A(x) = 1 + x * A(x/(1 - x)) / (1 - x^2).

1, 1, 1, 3, 7, 23, 81, 325, 1429, 6851, 35443, 196507, 1160633, 7266561, 48022313, 333776331, 2432140759, 18528143535, 147201596073, 1216952016245, 10448532393869, 92999784076875, 856739848236627, 8156691628658019, 80147320081510673, 811770418508099905

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..577

Formula

E.g.f.: exp(-x) * (2 * exp(exp(x) - 1) - 1).

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

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A186021(k).

a(n) = 2 * A000296(n) - (-1)^n.

Mathematica

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]
nmax = 25; CoefficientList[Series[Exp[-x] (2 Exp[Exp[x] - 1] - 1), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = a[1] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k] a[n - k - 1], {k, 1, n - 1}]; Table[a[n], {n, 0, 25}]

Crossrefs

Cf. A000110, A000296, A040027, A060719, A186021, A344489.

Sequence in context: A208591 A104088 A169650 * A136508 A184935 A099152

Adjacent sequences: A346768 A346769 A346770 * A346772 A346773 A346774

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 02 2021

Status

approved