A028379 a(n) = 6*(n+1)*(2*n+6)!/((n+3)!*(n+5)!).

0, 6, 28, 108, 396, 1430, 5148, 18564, 67184, 244188, 891480, 3268760, 12034980, 44482230, 165002460, 614106900, 2292665760, 8583849780, 32223863880, 121267584360, 457412818200, 1729020452796, 6548744132568, 24849948274088, 94460672942496, 359656297841400

Offset

-1,2

Comments

a(n) is the number of permutations pi of [n+4] such that s(pi) is one of 132456...(n+4), 231456...(n+4), 312456...(n+4), or 321456...(n+4) and s denotes West's stack-sorting map. - Colin Defant, Jan 14 2019

Links

Vincenzo Librandi, Table of n, a(n) for n = -1..1000

Formula

G.f.: (2 - 9*x + 6*x^2 + 2*x^3 + (5*x-2)*sqrt(1-4*x))/(x^4) = 6*x + 14*x^2*G(0); G(k) = 1 + 1/(k + 1 - 2*x*(k+1)*(k+2)*(2*k+9)/(2*x*(k+2)*(2*k+9) + (k+7)/G(k+1))); (continued fraction, 3-step ). - Sergei N. Gladkovskii, Jan 08 2012

-(n+4)*(n-1)*a(n) + 2*n*(2*n+3)*a(n-1) = 0, n > 0. - R. J. Mathar, Dec 15 2015

G.f.: x*C(x)^6 + 3*(1+C(x))C(x)^4, where C(x) = (1-sqrt(1-4x))/(2x) is the Catalan function. - Colin Defant, Jan 14 2019

a(n) = 3*A120989(n+1) + A003517(n+1). - Colin Defant, Jan 14 2019

Mathematica

Table[6 (n + 1) (2 n + 6)! / ((n + 3)! (n + 5)!), {n, -1, 25}] (* Vincenzo Librandi, Jan 15 2019 *)

Prog

(Magma) [6*(n+1)*Factorial(2*n+6)/(Factorial(n+3)*Factorial(n+5)): n in [-1..40]]; // Vincenzo Librandi, Jan 15 2019

Crossrefs

Cf. A003517, A120989.

Sequence in context: A352739 A117999 A234617 * A332751 A263942 A326138

Adjacent sequences: A028376 A028377 A028378 * A028380 A028381 A028382

Keyword

nonn

Author

N. J. A. Sloane, Grisha Berkolaiko (grisha(AT)ORY.ph.biu.ac.il)

Status

approved