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A274117 a(n) = ((6n-5)!!!+(6n-4)!!!)/(6n-3). 2
1, 12, 1064, 252160, 115315200, 86449126400, 96313245952000, 149342026677043200, 307513455044956160000, 811744577542368870400000, 2672529840751688498380800000, 10735527449319396895332761600000, 51677469466519591978527317032960000, 293652804750537765304678163152896000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

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

FORMULA

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

EXAMPLE

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.

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 *)

PROG

(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))

CROSSREFS

Cf. A007661, A273889.

Sequence in context: A232912 A004812 A088671 * A295427 A260030 A160010

Adjacent sequences:  A274114 A274115 A274116 * A274118 A274119 A274120

KEYWORD

nonn

AUTHOR

Hong-Chang Wang, Brian Cheung, Jun 10 2016

STATUS

approved

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Last modified January 21 09:34 EST 2022. Contains 350476 sequences. (Running on oeis4.)