A132465 Let df(n,k) = Product_{i=0..k-1} (n-i) be the descending factorial and let P(m,n) = df(n-1,m-1)^2*(2*n-m)/((m-1)!*m!). Sequence gives P(7,n).

0, 0, 0, 0, 0, 0, 1, 63, 1232, 13104, 94500, 518364, 2317392, 8833968, 29630601, 89464375, 247351104, 634542272, 1526183568, 3470399856, 7511688000, 15564217536, 31016698713, 59686024167, 111284511184, 201628350000, 355896440900, 613353440700, 1034083486800

Offset

1,8

Links

Table of n, a(n) for n=1..29.

Formula

From Amiram Eldar, Jun 16 2026: (Start)

Sum_{n>=7} 1/a(n) = 7340032*log(2)/25 - 76315456/375.

Sum_{n>=7} (-1)^(n+1)/a(n) = 19292*Pi^2/5 - 1835008*Pi/25 + 144385507/750. (End)

Mathematica

df[n_, k_] := Product[n - i, {i, 0, k-1}]; P[m_, n_] := df[n - 1, m - 1]^2*(2*n - m)/((m - 1)!*m!); a[n_] := If[n < 7, 0, P[7, n]]; Array[a, 30] (* Amiram Eldar, Jun 16 2026 *)

Crossrefs

See A132458 for further information.

Sequence in context: A389915 A183076 A230660 * A202983 A107319 A243214

Adjacent sequences: A132462 A132463 A132464 * A132466 A132467 A132468

Keyword

nonn,easy

Author

Ottavio D'Antona (dantona(AT)dico.unimi.it), Oct 31 2007

Status

approved