2,2

a(n) = sum(((-1)^k/((k+1)!*(k+2)!))*(n!)*A028246(n, k+2)*A008955(k+1, k), k=0..n-2)

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);

Equals third left hand column of A161739 (RSEG2 triangle).

Other left hand columns are A129825 and A161743.

A008955 is a central factorial number triangle.

A028246 is Worpitzky's triangle.

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.

Sequence in context: A155366 A135039 A015634 this_sequence A041301 A138989 A071400

Adjacent sequences: A161739 A161740 A161741 this_sequence A161743 A161744 A161745

easy,sign

Johannes W. Meijer & Nico Baken (meijgia(AT)hotmail.com and n.h.g.baken(AT)tudelft.nl), Jun 18 2009