A343523 a(0) = 1; a(n) = 2 * Sum_{k=1..n} binomial(n,k) * a(k-1).

1, 2, 8, 34, 164, 878, 5136, 32490, 220476, 1594470, 12223016, 98876322, 840804820, 7491247006, 69730182720, 676390547034, 6821988655468, 71398971351510, 774032400213336, 8677733804696594, 100459693769214980, 1199306075189097230, 14746332963835756400, 186534818943430728906

Offset

0,2

Links

Georg Fischer, Table of n, a(n) for n = 0..400

Formula

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

Mathematica

a[0] = 1; a[n_] := a[n] = 2 Sum[Binomial[n, k] a[k - 1], {k, 1, n}]; Table[a[n], {n, 0, 23}]
nmax = 23; A[_] = 0; Do[A[x_] = 1 + 2 x A[x/(1 - x)]/(1 - x)^2 + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Crossrefs

Cf. A001861, A004123, A035009, A040027, A343975, A344735, A344840, A345077, A345078, A345081.

Sequence in context: A174808 A109972 A019023 * A030857 A030894 A030919

Adjacent sequences: A343520 A343521 A343522 * A343524 A343525 A343526

Keyword

nonn

Author

Ilya Gutkovskiy, Jun 07 2021

Status

approved