A274117 - OEIS

%I #12 Jun 11 2016 00:54:39

%S 1,12,1064,252160,115315200,86449126400,96313245952000,

%T 149342026677043200,307513455044956160000,811744577542368870400000,

%U 2672529840751688498380800000,10735527449319396895332761600000,51677469466519591978527317032960000,293652804750537765304678163152896000000

%N a(n) = ((6n-5)!!!+(6n-4)!!!)/(6n-3).

%C Sequence is similar to A273889, with a similar proof of divisibility.

%H Brian Cheung, <a href="/A274117/b274117.txt">Table of n, a(n) for n = 1..100</a>

%F a(n) = ((6n-5)!!!+(6n-4)!!!)/(6n-3).

%e a(1) = (1+2)/3 = 1;

%e a(2) = (1*4*7+2*5*8)/9 = 12;

%e a(3) = (1*4*7*10*13+2*5*8*11*14)/15 = 1064.

%t B[n_, k_] := (Product[k (i - 1) + 1, {i, 2 n - 1}] + Product[k (i - 1) + 2, {i, 2 n - 1}])/(2 k (n - 1) + 3); Table[B[n, 3], {n, 14}] (* _Michael De Vlieger_, Jun 10 2016 *)

%o (Python)

%o triplefac=lambda x:1 if x<2 else x*triplefac(x-3)

%o for i in range(1,101):

%o     print(i,(triplefac(6*i-5)+triplefac(6*i-4))//(6*i-3))

%Y Cf. A007661, A273889.

%K nonn

%O 1,2

%A _Hong-Chang Wang_, _Brian Cheung_, Jun 10 2016