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%I #6 Sep 22 2012 10:36:20
%S 1,10,73,425,1561,-2856,-73520,380160,15376416,-117209664,-7506967104,
%T 72162155520,7045087741056,-80246202992640,-11448278791372800,
%U 149576169325363200,30017051616972275712,-440857664887810867200
%N Fourth left hand column of the RSEG2 triangle A161739.
%F a(n) = sum(((-1)^k/((k+2)!*(k+3)!))*(n!)*A028246(n, k+3)*A008955(k+2, k), k = 0..n-3).
%p nmax:=21; for n from 0 to nmax do A008955(n,0):=1 end do: for n from 0 to nmax do A008955(n,n):=(n!)^2 end do: for n from 1 to nmax do for m from 1 to n-1 do A008955(n,m):= A008955(n-1,m-1)*n^2+A008955(n-1,m) end do: end do: for n from 1 to nmax do A028246(n,1):=1 od: for n from 1 to nmax do A028246(n,n):=(n-1)! od: for n from 3 to nmax do for m from 2 to n-1 do A028246(n,m):=m*A028246(n-1,m)+(m-1)*A028246(n-1,m-1) od: od: for n from 3 to nmax do a(n) := sum(((-1)^k/((k+2)!*(k+3)!))*(n!)*A028246(n,k+3)* A008955(k+2,k), k=0..n-3) od: seq(a(n),n=3..nmax);
%Y Equals fourth left hand column of A161739 (RSEG2 triangle).
%Y Other left hand columns are A129825 and A161742.
%Y A008955 is a central factorial number triangle.
%Y A028246 is Worpitzky's triangle.
%Y A001710 (n!/2!), A001715 (n!/3!), A001720 (n!/4!), A001725 (n!/5!), A001730 (n!/6!), A049388 (n!/7!), A049389 (n!/8!), A049398 (n!/9!), A051431 (n!/10!) appear in Maple program.
%K easy,sign
%O 3,2
%A _Johannes W. Meijer_ & Nico Baken (n.h.g.baken(AT)tudelft.nl), Jun 18 2009
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