A196154 Binomial transform of A004111.

0, 1, 3, 7, 16, 38, 95, 250, 689, 1972, 5809, 17484, 53497, 165845, 519681, 1643112, 5234728, 16785774, 54128870, 175409177, 570906174, 1865364061, 6116175260, 20117351296, 66361157675, 219484396545, 727692105683, 2418048043653, 8051628061939, 26862111773042, 89779489887570, 300568375668272, 1007841476081366

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) ~ c * d^n / n^(3/2), where d = 1 + A246169 = 3.51754035263200389079535459..., c = 0.59875012586719098912050580024... - 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)*binomial(n, k), k=0..n):
seq(a(n), n=0..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]*Binomial[n, k], {k, 0, n}]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 12 2016, after Alois P. Heinz *)

Crossrefs

Cf. A004111, A196161.

Sequence in context: A293065 A211278 A364625 * A227235 A304937 A152090

Adjacent sequences: A196151 A196152 A196153 * A196155 A196156 A196157

Keyword

nonn

Author

N. J. A. Sloane, Oct 27 2011

Status

approved