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A084915 a(n) = (n!)^2*n. 3
0, 1, 8, 108, 2304, 72000, 3110400, 177811200, 13005619200, 1185137049600, 131681894400000, 17526860144640000, 2753310393630720000, 504085244567224320000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Used to prove that Sum_{n>=1} 1/A002378(n) = 1. Examining Sum_{n=1..k} 1/A002378(n) gives 1/2, 1/2 + 1/6, 1/2 + 1/6 + 1/12. Simplifying gives 1/2, 8/12, 108/144, where the numerators are this sequence and the denominators are A010790. Therefore we have k!^2*k/k!(k+1)! = k*k!/(k+1)! = k/(k+1), which tends to 1 as k tends to infinity.

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) = n!*(n+1)! - n!^2.

a(n) = det(PS(i+2,j+1), 1 <= i,j <= n-1), where PS(n,k) are Legendre-Stirling numbers of the second kind (A071951) and n > 0. [Mircea Merca, Apr 06 2013]

EXAMPLE

a(3) = 3!^2*3 = 36*3 = 108.

PROG

(PARI) for(n=1, 50, print1(n!^2*n", "))

CROSSREFS

Cf. A002378, A010790, A071951.

Sequence in context: A336828 A184267 A099699 * A138456 A267660 A273057

Adjacent sequences:  A084912 A084913 A084914 * A084916 A084917 A084918

KEYWORD

nonn

AUTHOR

Jon Perry, Jul 14 2003

STATUS

approved

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Last modified August 7 09:16 EDT 2020. Contains 336274 sequences. (Running on oeis4.)