cp's OEIS Frontend

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.

%I A001194 M2826 N1139 #36 Nov 27 2024 11:50:56
%S A001194 3,9,54,450,4725,59535,873180,14594580,273648375,5685805125,
%T A001194 129636356850,3217338674550,86331921100425,2490343877896875,
%U A001194 76844896803675000,2525635608280785000,88081541838792376875,3248654513701342370625
%N 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.
%C A001194 Old name was: Expansion of an integral.
%D A001194 L. Comtet, Advanced Combinatorics, Reidel, 1974, pp. 166-167.
%D A001194 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001194 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001194 Reinis Cirpons, James East, and James D. Mitchell, <a href="https://arxiv.org/abs/2411.14693">Transformation representations of diagram monoids</a>, arXiv:2411.14693 [math.RA], 2024. See p. 3.
%H A001194 Louis Comtet, <a href="https://www.jstor.org/stable/43667287">Fonctions génératrices et calcul de certaines intégrales</a>, Publikacije Elektrotechnickog faculteta - Serija Matematika i Fizika, No. 181/196 (1967), 77-87; see p. 85.
%F A001194 a(n) = (2*n - 1)*a(n-1) - 3*(n - 1)*(2*n - 7)!! for n > 3. - _Sean A. Irvine_, Mar 23 2012
%F A001194 a(n) = 3*n*(n-1)*(2*n-4)!/(2^(n-1)*(n-2)!) for n >= 2. - _Vaclav Kotesovec_, Jan 05 2014
%F A001194 a(n) = binomial(-1/2, 2) * binomial(-1/2, n-2) * (-1)^n * n! * 2^n for n >= 2. - _Petros Hadjicostas_, May 13 2020
%F A001194 a(n) ~ sqrt(2)*(3/8)*(2*n/e)^n. - _Peter Luschny_, May 14 2020
%t A001194 Table[3*n*(n-1)*(2*n-4)!/(2^(n-1)*(n-2)!),{n,2,20}] (* _Vaclav Kotesovec_, Jan 05 2014 *)
%K A001194 nonn
%O A001194 2,1
%A A001194 _N. J. A. Sloane_
%E A001194 More terms from _Sean A. Irvine_, Mar 22 2012
%E A001194 New name by _Petros Hadjicostas_, May 13 2020