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A114633 a(n) = (n+1)*(n+2)/2 * Sum_{k=0..floor(n/2)} n!/(n-2*k)!. 1

%I #20 Sep 03 2017 15:24:03

%S 1,3,18,70,555,2961,31108,213228,2799765,23455135,369569046,

%T 3659001138,67261566463,768390239085,16142775951240,209002145031256,

%U 4939689441079593,71478733600689723,1877081987610245530,30021068112289683870,867211878275933435091,15190660464818580038473

%N a(n) = (n+1)*(n+2)/2 * Sum_{k=0..floor(n/2)} n!/(n-2*k)!.

%C Formula was found by _Paul D. Hanna_.

%C Related to logarithmic numbers A002104.

%H Vincenzo Librandi, <a href="/A114633/b114633.txt">Table of n, a(n) for n = 0..450</a>

%F a(n) = A087208(n)*(n+1)*(n+2)/2. - _Paul D. Hanna_

%F E.g.f.: exp(x)/(1-x^2)*(x^2/2) (with offset 2). - _Zerinvary Lajos_, Apr 03 2009

%p a:= n-> (n+1)*(n+2)/2*sum(n!/(n-2*k)!,k=0..floor(n/2)): seq(a(n), n=0..20);

%t Rest[Rest[With[{nn=25}, CoefficientList[Series[Exp[x]/(1 - x^2)(x^2/2), {x, 0, nn}], x] Range[0, nn]!]]] (* _Vincenzo Librandi_, Sep 03 2017 *)

%Y Cf. A002104, A087208.

%K nonn

%O 0,2

%A _Creighton Dement_, Feb 17 2006

%E More terms from _Vincenzo Librandi_, Sep 03 2017

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)