A274117 a(n) = ((6n-5)!!!+(6n-4)!!!)/(6n-3).

1, 12, 1064, 252160, 115315200, 86449126400, 96313245952000, 149342026677043200, 307513455044956160000, 811744577542368870400000, 2672529840751688498380800000, 10735527449319396895332761600000, 51677469466519591978527317032960000, 293652804750537765304678163152896000000

Offset: 1

Author

Hong-Chang Wang, Brian Cheung, Jun 10 2016

Keywords

• nonn

Comments

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

Examples

			a(1) = (1+2)/3 = 1;
a(2) = (1*4*7+2*5*8)/9 = 12;
a(3) = (1*4*7*10*13+2*5*8*11*14)/15 = 1064.
		

Links

• Brian Cheung, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A007661, A273889.

Programs

Mathematica

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 *)

Python

triplefac=lambda x:1 if x<2 else x*triplefac(x-3)
for i in range(1,101):
    print(i,(triplefac(6*i-5)+triplefac(6*i-4))//(6*i-3))

Formula

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