A004995 - OEIS

%I #14 Sep 08 2022 08:44:33

%S 1,-30,-90,-1260,-24570,-560196,-14004900,-372130200,-10326613050,

%T -296029574100,-8703269478540,-261098084356200,-7963491572864100,

%U -246255662483951400,-7704284297712193800,-243455383807705324080

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

%H G. C. Greubel, <a href="/A004995/b004995.txt">Table of n, a(n) for n = 0..635</a>

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

%F 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

%F a(n) = 6^(2*n) * binomial(n-11/6, n). - _G. C. Greubel_, Aug 20 2019

%F D-finite with recurrence: n*a(n) +6*(-6*n+11)*a(n-1)=0. - _R. J. Mathar_, Jan 17 2020

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

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

%o (PARI) vector(20, n, n--; 6^n*prod(j=0,n-1, 6*j-5)/n! ) \\ _G. C. Greubel_, Aug 20 2019

%o (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

%o (Sage) [6^(2*n)*rising_factorial(-5/6, n)/factorial(n) for n in (0..20)] # _G. C. Greubel_, Aug 20 2019

%o (GAP) List([0..20], n-> 6^n*Product([0..n-1], k-> 6*k-5)/Factorial(n) ); # _G. C. Greubel_, Aug 20 2019

%K sign,easy

%O 0,2

%A Joe Keane (jgk(AT)jgk.org)