The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A028379

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A028379

a(n) = 6*(n+1)*(2*n+6)!/((n+3)!*(n+5)!).
(history; published version)

#25 by Charles R Greathouse IV at Thu Sep 08 08:44:50 EDT 2022

PROG

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

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#24 by N. J. A. Sloane at Sun Jan 20 06:50:52 EST 2019

STATUS

proposed

approved

#23 by Vincenzo Librandi at Tue Jan 15 01:31:15 EST 2019

STATUS

editing

proposed

#22 by Vincenzo Librandi at Tue Jan 15 01:30:59 EST 2019

LINKS

Vincenzo Librandi, <a href="/A028379/b028379.txt">Table of n, a(n) for n = -1..1000</a>

#21 by Vincenzo Librandi at Tue Jan 15 01:23:57 EST 2019

DATA

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

FORMULA

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

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

Cf. A003517, A120989.

STATUS

proposed

editing

#20 by Jon E. Schoenfield at Mon Jan 14 23:34:06 EST 2019

STATUS

editing

proposed

Discussion

Mon Jan 14

23:34

Jon E. Schoenfield: (sorry, in two of three cases)  :-)

#19 by Jon E. Schoenfield at Mon Jan 14 23:33:29 EST 2019

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

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

CROSSREFS

Equals 3*A120989(n+1) + A003517(n+1) . -_ _Colin Defant_, Jan 14 2019

STATUS

proposed

editing

Discussion

Mon Jan 14

23:34

Jon E. Schoenfield: Corrected your signatures (there was a missing space between the dash and your name in each case).

#18 by Colin Defant at Mon Jan 14 20:37:45 EST 2019

STATUS

editing

proposed

#17 by Colin Defant at Mon Jan 14 18:15:54 EST 2019

COMMENTS

CROSSREFS

Equals 3*A120989(n+1)+A003517(n+1) -_Colin Defant_, Jan 14 2019

STATUS

proposed

editing

#16 by Colin Defant at Mon Jan 14 18:14:35 EST 2019

STATUS

editing

proposed