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A072374 a(1) = 1; a(n) = 1 + Sum_{i=1..n} Product_{j=i..2*i-1} (n-j). 10

%I #15 Feb 11 2014 05:08:08

%S 1,2,3,6,11,24,51,122,291,756,1979,5526,15627,46496,140451,442194,

%T 1414931,4687212,15785451,54764846,193129659,698978136,2570480147,

%U 9672977706,36967490691,144232455524,571177352091,2304843053382,9434493132011,39289892366736

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

%C A122852 is another version of the same sequence. - _R. J. Mathar_, Jun 18 2008

%H Vincenzo Librandi, <a href="/A072374/b072374.txt">Table of n, a(n) for n = 1..200</a>

%F 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

%F Recurrence: 2*a(n) = 3*a(n-1) + (n-1)*a(n-2) - (n-1)*a(n-3). - _Vaclav Kotesovec_, Feb 08 2014

%F 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

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

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jul 19 2002

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Last modified June 15 09:24 EDT 2024. Contains 373407 sequences. (Running on oeis4.)