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%I #8 Jul 26 2015 01:47:20
%S 0,2,7,22,79,356,2019,13826,109855,986920,9865123,108507158,
%T 1302065439,16926805676,236975181187,3554627504842,56874039618751,
%U 966858672535760,17403456103546563,330665665962928286,6613313319249128575
%N a(n) = Sum_{k=1..n} (P(n,k) + C(n,k)).
%F a(n) = Sum_{k=1..n} n!(k!+1) / k!(n-k)! = Sum_{k=1..n} P(n, k)+2^n-1 = A007526(n) - A000225(n) - 1 = A097656(n) - 2.
%F Conjecture: a(n) +(-n-6)*a(n-1) +(6*n+7)*a(n-2) +(-13*n+14)*a(n-3) +4*(3*n-8)*a(n-4) +4*(-n+4)*a(n-5)=0. - _R. J. Mathar_, May 29 2013
%e a(2) = 7 because P(2,1) = 2, P(2,2) = 2 while C(2,1)= 2, C(2,2) = 1 and 2 + 2 + 2 + 1 = 7.
%p A097967 := proc(n)
%p add(n!*(k!+1)/k!/(n-k)!,k=1..n) ;
%p end proc: # _R. J. Mathar_, May 29 2013
%t f[n_] := Sum[n!(k! + 1)/(k!(n - k)!), {k, n}]; Table[ f[n], {n, 0, 20}] (* _Robert G. Wilson v_, Sep 24 2004 *)
%Y Cf. A097656, A007526, A000225.
%K nonn
%O 0,2
%A _Ross La Haye_, Sep 21 2004
%E Edited by _Robert G. Wilson v_, Sep 24 2004
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