A006957 Self-convolution of numbers of preferential arrangements.

1, 2, 7, 32, 185, 1310, 11067, 109148, 1234045, 15752858, 224169407, 3518636504, 60381131265, 1124390692886, 22577494959427, 486212633129300, 11177317486573445, 273173247028616594, 7072436847620016327, 193351544314753174736, 5565941751233499986185

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) ~ n! / (log(2))^(n+1). - Vaclav Kotesovec, Nov 08 2014

G.f.: (Sum_{j>=0} j!*x^j / Product_{k=1..j} (1 - k*x))^2. - Ilya Gutkovskiy, Apr 06 2019

Maple

f:= proc(n) option remember; `if`(n<=1, 1,
      add(binomial(n, k) *f(n-k), k=1..n))
    end:
a:= n-> add(f(k)*f(n-k), k=0..n):
seq(a(n), n=0..25);  # Alois P. Heinz, Feb 02 2009

Mathematica

t[n_] := Sum[StirlingS2[n, k]*k!, {k, 0, n}]; Table[Sum[t[k]*t[n-k], {k, 0, n}], {n, 0, 20}] (* Jean-François Alcover, Apr 09 2014, after Emanuele Munarini *)

Prog

(Maxima) t(n):=sum(stirling2(n, k)*k!, k, 0, n);
makelist(sum(t(k)*t(n-k), k, 0, n), n, 0, 20);
\\ Emanuele Munarini, Oct 02 2012

Crossrefs

Cf. A000670, A217388, A217389.

Sequence in context: A006154 A352435 A000987 * A189780 A195983 A079265

Adjacent sequences: A006954 A006955 A006956 * A006958 A006959 A006960

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Alois P. Heinz, Feb 02 2009

Status

approved