A004992 a(n) = (3^n/n!) * Product_{k=0..n-1} (3*k + 5).

1, 15, 180, 1980, 20790, 212058, 2120580, 20902860, 203802885, 1970094555, 18912907728, 180532301040, 1715056859880, 16227076443480, 152998149324240, 1438182603647856, 13482961909198650, 126105349621328550, 1176983263132399800, 10964528293391303400, 101970113128539121620

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for sequences related to the Josephus Problem

Formula

G.f.: (1 - 9*x)^(-5/3).

a(n) ~ (3/2)*Gamma(2/3)^-1*n^(2/3)*3^(2*n)*(1 + (5/9)*n^-1 - ...).

D-finite with recurrence: n*a(n) +3*(-3*n-2)*a(n-1)=0. - R. J. Mathar, Jan 17 2020

Sum_{n>=0} 1/a(n) = sqrt(3)*Pi/2 - 3*log(3)/2. - Amiram Eldar, Dec 02 2022

Maple

a:= n-> (3^n/n!)*mul(3*k+5, k=0..n-1): seq(a(n), n=0..25); # G. C. Greubel, Aug 22 2019

Mathematica

Table[9^n*Pochhammer[5/3, n]/n!, {n, 0, 25}] (* G. C. Greubel, Aug 22 2019 *)
Table[3^n/n! Product[3k+5, {k, 0, n-1}], {n, 0, 20}] (* Harvey P. Dale, Jan 07 2023 *)

Prog

(PARI) a(n) = 3^n*prod(k=0, n-1, 3*k+5)/n!;
vector(25, n, a(n-1)) \\ G. C. Greubel, Aug 22 2019
(Magma) [1] cat [3^n*&*[3*k+5: k in [0..n-1]]/Factorial(n): n in [1..25]]; // G. C. Greubel, Aug 22 2019
(Sage) [9^n*rising_factorial(5/3, n)/factorial(n) for n in (0..25)] # G. C. Greubel, Aug 22 2019
(GAP) List([0..25], n-> 3^n*Product([0..n-1], k-> 3*k+5)/Factorial(n) ); # G. C. Greubel, Aug 22 2019

Crossrefs

Cf. A004988, A004989, A004990, A004991.

Sequence in context: A244604 A001717 A293476 * A055084 A005461 A373759

Adjacent sequences: A004989 A004990 A004991 * A004993 A004994 A004995

Keyword

nonn,easy

Author

Joe Keane (jgk(AT)jgk.org)

Extensions

Terms a(16) onward added by G. C. Greubel, Aug 22 2019

Status

approved