A072374 a(1) = 1; a(n) = 1 + Sum_{i=1..n} Product_{j=i..2*i-1} (n-j).

1, 2, 3, 6, 11, 24, 51, 122, 291, 756, 1979, 5526, 15627, 46496, 140451, 442194, 1414931, 4687212, 15785451, 54764846, 193129659, 698978136, 2570480147, 9672977706, 36967490691, 144232455524, 571177352091, 2304843053382, 9434493132011, 39289892366736

Offset

1,2

Comments

A122852 is another version of the same sequence. - R. J. Mathar, Jun 18 2008

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Formula

The sequence 1, 1, 2, 3, .. has a(n)=sum{k=0..floor(n/2), C(n-k, k)k!} (diagonal sums of permutation triangle A008279). - Paul Barry, May 12 2004

Recurrence: 2*a(n) = 3*a(n-1) + (n-1)*a(n-2) - (n-1)*a(n-3). - Vaclav Kotesovec, Feb 08 2014

a(n) ~ sqrt(Pi) * exp(sqrt(n/2) - n/2 + 1/8) * n^((n+1)/2) / 2^(n/2+1) * (1 + 37/(48*sqrt(2*n))). - Vaclav Kotesovec, Feb 08 2014

Mathematica

Table[Sum[Binomial[n-k, k]*k!, {k, 0, Floor[n/2]}], {n, 1, 20}] (* Vaclav Kotesovec, Feb 08 2014 *)

Crossrefs

Sequence in context: A036648 A047750 A072187 * A122852 A192573 A284994

Adjacent sequences: A072371 A072372 A072373 * A072375 A072376 A072377

Keyword

nonn

Author

N. J. A. Sloane, Jul 19 2002

Status

approved