This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A161742 #9 Jun 02 2025 01:44:39 %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 %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 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. %K A161742 easy,sign %O A161742 2,2 %A A161742 _Johannes W. Meijer_ & Nico Baken (n.h.g.baken(AT)tudelft.nl), Jun 18 2009