A355109 a(n) = 1 + Sum_{k=1..n-1} binomial(n-1,k) * 2^(k-1) * a(k).

1, 1, 2, 7, 44, 493, 9974, 372403, 26247008, 3559692121, 942403603562, 491777568765151, 508938530329020692, 1048381120745440503877, 4307758467916752367544414, 35349370769806113877653011083, 579693879415731511179957972407624

Offset: 0

Author

Ilya Gutkovskiy, Jun 19 2022

Keywords

• nonn

Crossrefs

Cf. A000110, A126443, A352859, A352860.

Programs

Maple

a:= proc(n) option remember; 1+add(a(k)*
      binomial(n-1, k)*2^(k-1), k=1..n-1)
    end:
seq(a(n), n=0..16);  # Alois P. Heinz, Jun 19 2022

Mathematica

a[n_] := a[n] = 1 + Sum[Binomial[n - 1, k] 2^(k - 1) a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 16}]
nmax = 16; A[] = 0; Do[A[x] = (2 - x + x A[2 x/(1 - x)])/(2 (1 - x)) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

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