A004995 a(n) = (6^n/n!) * Product_{k=0..n-1} (6*k - 5).

1, -30, -90, -1260, -24570, -560196, -14004900, -372130200, -10326613050, -296029574100, -8703269478540, -261098084356200, -7963491572864100, -246255662483951400, -7704284297712193800, -243455383807705324080

Offset

0,2

Links

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

Formula

G.f.: (1 - 36*x)^(5/6).

a(n) ~ -(5/6)*Gamma(1/6)^-1*n^(-11/6)*6^(2*n)*(1 + (55/72)*n^-1 + ...). - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

a(n) = 6^(2*n) * binomial(n-11/6, n). - G. C. Greubel, Aug 20 2019

D-finite with recurrence: n*a(n) +6*(-6*n+11)*a(n-1)=0. - R. J. Mathar, Jan 17 2020

Maple

seq(6^n*product(6*k-5, k = 0..n-1)/n!, n = 0..20); # G. C. Greubel, Aug 20 2019

Mathematica

Table[6^(2*n)*Pochhammer[-5/6, n]/n!, {n, 0, 20}] (* G. C. Greubel, Aug 20 2019 *)

Prog

(PARI) vector(20, n, n--; 6^n*prod(j=0, n-1, 6*j-5)/n! ) \\ G. C. Greubel, Aug 20 2019
(Magma) [1] cat [6^n*(&*[6*k-5: k in [0..n-1]])/Factorial(n): n in [1..20]]; // G. C. Greubel, Aug 20 2019
(Sage) [6^(2*n)*rising_factorial(-5/6, n)/factorial(n) for n in (0..20)] # G. C. Greubel, Aug 20 2019
(GAP) List([0..20], n-> 6^n*Product([0..n-1], k-> 6*k-5)/Factorial(n) ); # G. C. Greubel, Aug 20 2019

Crossrefs

Sequence in context: A039462 A370495 A138018 * A042772 A042770 A306121

Adjacent sequences: A004992 A004993 A004994 * A004996 A004997 A004998

Keyword

sign,easy

Author

Joe Keane (jgk(AT)jgk.org)

Status

approved