A004998 a(n) = (6^n/n!) * Product_{k=0..n-1} ( 6*k + 11 ).

1, 66, 3366, 154836, 6735366, 282885372, 11598300252, 467245810152, 18573020953542, 730538824172652, 28491014142733428, 1103379274982221848, 42480102086815541148, 1627314679941087653208, 62070431363467200486648, 2358676391811753618492624, 89334868339870168300408134

Offset

0,2

Links

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

Formula

G.f.: (1 - 36*x)^(-11/6).

a(n) ~ 6/5*Gamma(5/6)^-1*n^(5/6)*6^(2*n)*{1 + 55/72*n^-1 - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

D-finite with recurrence: n*a(n) +6*(-6*n-5)*a(n-1)=0. - R. J. Mathar, Jan 17 2020

Maple

a:= n-> (6^n/n!)*product(6*k+11, k=0..n-1); seq(a(n), n=0..20); # G. C. Greubel, Aug 22 2019

Mathematica

CoefficientList[Series[(1-36x)^(-11/6), {x, 0, 20}], x] (* or *) Table[(36^(n-1) Pochhammer[11/6, n-1])/Gamma[n], {n, 20}] (* Harvey P. Dale, Jul 24 2011 *)

Prog

(PARI) a(n) = (6^n/n!)*prod(k=0, n-1, 6*k+11);
vector(20, n, n--; a(n)) \\ G. C. Greubel, Aug 22 2019
(Magma) [1] cat [6^n*(&*[6*k+11: k in [0..n-1]])/Factorial(n): n in [1..20]]; // G. C. Greubel, Aug 22 2019
(Sage) [6^(2*n)*rising_factorial(11/6, 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+11)/Factorial(n) ); # G. C. Greubel, Aug 22 2019

Crossrefs

Sequence in context: A138875 A138877 A265454 * A239409 A295592 A097316

Adjacent sequences: A004995 A004996 A004997 * A004999 A005000 A005001

Keyword

nonn,easy

Author

Joe Keane (jgk(AT)jgk.org)

Extensions

Terms a(14) onward added by G. C. Greubel, Aug 22 2019

Status

approved