%I A161742
%S A161742 1,4,13,30,14,504,736,44640,104544,10644480,33246720,5425056000,
%T A161742 20843695872,5185511654400,23457840537600,8506857655296000,
%U A161742 44092609863966720,22430879475779174400,130748316971139072000
%V A161742 1,4,13,30,-14,-504,736,44640,-104544,-10644480,33246720,5425056000,
%W A161742 -20843695872,-5185511654400,23457840537600,8506857655296000,
%X A161742 -44092609863966720,-22430879475779174400,130748316971139072000
%N A161742 Third left hand column of the RSEG2 triangle A161739
%F A161742 a(n) = sum(((-1)^k/((k+1)!*(k+2)!))*(n!)*A028246(n, k+2)*A008955(k+1,
k), k=0..n-2)
%p A161742 restart; 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 2 to nmax do a(n):=sum(((-1)^k/((k+1)!*(k+2)!))
*(n!)*A028246(n,k+2)* A008955(k+1,k),k=0..n-2) od: seq(a(n),n=2..nmax);
%Y A161742 Equals third left hand column of A161739 (RSEG2 triangle).
%Y A161742 Other left hand columns are A129825 and A161743.
%Y A161742 A008955 is a central factorial number triangle.
%Y A161742 A028246 is Worpitzky's triangle.
%Y A161742 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.
%Y A161742 Sequence in context: A155366 A135039 A015634 this_sequence A041301 A138989
A071400
%Y A161742 Adjacent sequences: A161739 A161740 A161741 this_sequence A161743 A161744
A161745
%K A161742 easy,sign
%O A161742 2,2
%A A161742 Johannes W. Meijer & Nico Baken (meijgia(AT)hotmail.com and n.h.g.baken(AT)tudelft.nl),
Jun 18 2009
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