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 A161743 Fourth left hand column of the RSEG2 triangle A161739. 5
 1, 10, 73, 425, 1561, -2856, -73520, 380160, 15376416, -117209664, -7506967104, 72162155520, 7045087741056, -80246202992640, -11448278791372800, 149576169325363200, 30017051616972275712, -440857664887810867200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS FORMULA a(n) = sum(((-1)^k/((k+2)!*(k+3)!))*(n!)*A028246(n, k+3)*A008955(k+2, k), k = 0..n-3). MAPLE 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); CROSSREFS Equals fourth left hand column of A161739 (RSEG2 triangle). Other left hand columns are A129825 and A161742. 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: A240275 A181402 A003366 * A016211 A055424 A243878 Adjacent sequences:  A161740 A161741 A161742 * A161744 A161745 A161746 KEYWORD easy,sign AUTHOR Johannes W. Meijer & Nico Baken (n.h.g.baken(AT)tudelft.nl), Jun 18 2009 STATUS approved

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Last modified December 1 22:24 EST 2020. Contains 338858 sequences. (Running on oeis4.)