A196161 Binomial transform of {A004111(n), n >= 1}.

1, 2, 4, 9, 22, 57, 155, 439, 1283, 3837, 11675, 36013, 112348, 353836, 1123431, 3591616, 11551046, 37343096, 121280307, 395496997, 1294457887, 4250811199, 14001176036, 46243806379, 153123238870, 508207709138, 1690355937970, 5633580018286, 18810483711103, 62917378114528, 210788885780702, 707273100413094

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

a(n) ~ c * d^n / n^(3/2), where d = 1 + A246169 = 3.51754035263200389079535459..., c = 0.428531715886712592684516703... - Vaclav Kotesovec, Oct 30 2017

Maple

with(numtheory):
b:= proc(n) option remember; `if`(n<2, n, add(b(n-k)*add(
      b(d)*d*(-1)^(k/d+1), d=divisors(k)), k=1..n-1)/(n-1))
    end:
a:= n-> add(b(k+1)*binomial(n-1, k), k=0..n-1):
seq(a(n), n=1..50);  # Alois P. Heinz, Feb 24 2015

Mathematica

b[n_] := b[n] = If[n < 2, n, Sum[b[n - k]*Sum[ b[d]*d*(-1)^(k/d + 1), {d, Divisors[k]}], {k, 1, n-1}]/(n-1)]; a[n_] := Sum[b[k+1]*Binomial[n-1, k], {k, 0, n-1}]; Table[a[n], {n, 1, 50}] (* Jean-François Alcover, Feb 12 2016, after Alois P. Heinz *)

Crossrefs

Cf. A004111, A196154.

Sequence in context: A105633 A287709 A348202 * A333069 A249561 A099241

Adjacent sequences: A196158 A196159 A196160 * A196162 A196163 A196164

Keyword

nonn

Author

N. J. A. Sloane, Oct 27 2011

Status

approved