A004997 a(n) = (6^n/n!) * Product_{k=0..n-1} (6*k + 7).

1, 42, 1638, 62244, 2334150, 86830380, 3212724060, 118411829640, 4351634739270, 159559940439900, 5839893820100340, 213421574152757880, 7789887456575662620, 284031281108989544760, 10346853811827476273400, 376625478750520136351760, 13699751789550169959795270

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..635

Formula

G.f.: (1 - 36*x)^(-7/6).

a(n) ~ 6*Gamma(1/6)^-1*n^(1/6)*6^(2*n)*(1 + (7/72)*n^-1 - ...). - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

D-finite with recurrence: n*a(n) +6*(-6*n-1)*a(n-1)=0. - R. J. Mathar, Jan 17 2020

Maple

a:= n-> (6^n/n!)*mul(6*k+7, k=0..n-1); seq(a(n), n=0..20); # G. C. Greubel, Aug 22 2019

Mathematica

Table[6^(2*n)*Pochhammer[7/6, n]/n!, {n, 0, 20}] (* G. C. Greubel, Aug 22 2019 *)

Prog

(PARI) a(n) = 6^n*prod(k=0, n-1, 6*k+7)/n!;
vector(20, n, a(n-1)) \\ G. C. Greubel, Aug 22 2019
(Magma) [1] cat [6^n*&*[6*k+7: k in [0..n-1]]/Factorial(n): n in [1..20]]; // G. C. Greubel, Aug 22 2019
(Sage) [6^(2*n)*rising_factorial(7/6, n)/factorial(n) for n in (0..20)] # G. C. Greubel, Aug 22 2019
(GAP) List([0..20], n-> 6^n*Product([0..n-1], k-> 6*k+7)/Factorial(n) ); # G. C. Greubel, Aug 22 2019

Crossrefs

Sequence in context: A270410 A000502 A215545 * A120815 A162879 A163225

Adjacent sequences: A004994 A004995 A004996 * A004998 A004999 A005000

Keyword

nonn,easy

Author

Joe Keane (jgk(AT)jgk.org)

Status

approved