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A274117
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a(n) = ((6n-5)!!!+(6n-4)!!!)/(6n-3).
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2
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1, 12, 1064, 252160, 115315200, 86449126400, 96313245952000, 149342026677043200, 307513455044956160000, 811744577542368870400000, 2672529840751688498380800000, 10735527449319396895332761600000, 51677469466519591978527317032960000, 293652804750537765304678163152896000000
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OFFSET
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1,2
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COMMENTS
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Sequence is similar to A273889, with a similar proof of divisibility.
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LINKS
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FORMULA
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a(n) = ((6n-5)!!!+(6n-4)!!!)/(6n-3).
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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