A001194 a(n) = A059366(n,n-2) = A059366(n,2) for n >= 2, where the triangle A059366 arises in the expansion of a trigonometric integral. (Formerly M2826 N1139)

3, 9, 54, 450, 4725, 59535, 873180, 14594580, 273648375, 5685805125, 129636356850, 3217338674550, 86331921100425, 2490343877896875, 76844896803675000, 2525635608280785000, 88081541838792376875, 3248654513701342370625

Offset

2,1

Comments

Old name was: Expansion of an integral.

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, pp. 166-167.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=2..19.

Reinis Cirpons, James East, and James D. Mitchell, Transformation representations of diagram monoids, arXiv:2411.14693 [math.RA], 2024. See p. 3.

Louis Comtet, Fonctions génératrices et calcul de certaines intégrales, Publikacije Elektrotechnickog faculteta - Serija Matematika i Fizika, No. 181/196 (1967), 77-87; see p. 85.

Formula

a(n) = (2*n - 1)*a(n-1) - 3*(n - 1)*(2*n - 7)!! for n > 3. - Sean A. Irvine, Mar 23 2012

a(n) = 3*n*(n-1)*(2*n-4)!/(2^(n-1)*(n-2)!) for n >= 2. - Vaclav Kotesovec, Jan 05 2014

a(n) = binomial(-1/2, 2) * binomial(-1/2, n-2) * (-1)^n * n! * 2^n for n >= 2. - Petros Hadjicostas, May 13 2020

a(n) ~ sqrt(2)*(3/8)*(2*n/e)^n. - Peter Luschny, May 14 2020

Mathematica

Table[3*n*(n-1)*(2*n-4)!/(2^(n-1)*(n-2)!), {n, 2, 20}] (* Vaclav Kotesovec, Jan 05 2014 *)

Crossrefs

Sequence in context: A212418 A337039 A025226 * A032179 A377340 A233189

Adjacent sequences: A001191 A001192 A001193 * A001195 A001196 A001197

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Mar 22 2012

New name by Petros Hadjicostas, May 13 2020

Status

approved