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A196154 Binomial transform of A004111. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Feb 12 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A004111, A196161.

Sequence in context: A323225 A293065 A211278 * A227235 A304937 A152090

Adjacent sequences:  A196151 A196152 A196153 * A196155 A196156 A196157

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 27 2011

STATUS

approved

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Last modified June 17 19:10 EDT 2019. Contains 324198 sequences. (Running on oeis4.)