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A243757
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a(n) = Product_{i=1..n} A060904(i).
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3
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1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 25, 25, 25, 25, 25, 125, 125, 125, 125, 125, 625, 625, 625, 625, 625, 15625, 15625, 15625, 15625, 15625, 78125, 78125, 78125, 78125, 78125, 390625, 390625, 390625, 390625, 390625, 1953125, 1953125, 1953125, 1953125, 1953125, 9765625
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OFFSET
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0,6
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COMMENTS
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This is the generalized factorial for A060904.
a(0) = 1 as it represents the empty product.
a(n) is the largest power of 5 that divides n!, or the order of a 5-Sylow subgroup of the symmetric group of degree n. - David Radcliffe, Sep 03 2021
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LINKS
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Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.
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FORMULA
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a(n) = Product_{i=1..n} A060904(i).
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MATHEMATICA
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Table[Product[5^IntegerExponent[k, 5], {k, 1, n}], {n, 0, 20}] (* G. C. Greubel, Dec 24 2016 *)
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PROG
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(Sage)
S=[0]+[5^valuation(i, 5) for i in [1..100]]
[prod(S[1:i+1]) for i in [0..99]]
(Haskell)
a243757 n = a243757_list !! n
a243757_list = scanl (*) 1 a060904_list
(PARI) a(n) = prod(k=1, n, 5^valuation(k, 5)); \\ G. C. Greubel, Dec 24 2016
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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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