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A034687
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Related to quintic factorial numbers A008548.
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6
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1, 15, 275, 5500, 115500, 2502500, 55412500, 1246781250, 28398906250, 653174843750, 15141780468750, 353308210937500, 8289154179687500, 195387205664062500, 4624163867382812500, 109823891850341796875
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 5^(n-1)*A008548(n)/n!, where A008548(n)=(5*n-4)(!^5) = Product_{j=1..n} (5*j-4).
G.f.: (-1 + (1-25*x)^(-1/5))/5.
E.g.f.: (1/5)*L_{-1/5}(25*x) - 1, where L_{k}(x) is the Laguerre polynomial. - Stefano Spezia, Aug 17 2019
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MAPLE
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seq(5^(n-1)*(product(5*k+1, k = 0..n-1))/factorial(n), n = 1..20); # G. C. Greubel, Aug 17 2019
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MATHEMATICA
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Table[5^(2*n-1)*Pochhammer[1/5, n]/n!, {n, 20}] (* G. C. Greubel, Aug 17 2019 *)
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PROG
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(PARI) vector(20, n, 5^(n-1)*prod(k=0, n-1, 5*k+1)/n!) \\ G. C. Greubel, Aug 17 2019
(Magma) [5^(n-1)*(&*[5*k+1: k in [0..n-1]])/Factorial(n): n in [1..20]]; // G. C. Greubel, Aug 17 2019
(Sage) [5^(n-1)*product(5*k+1 for k in (0..n-1))/factorial(n) for n in (1..20)] # G. C. Greubel, Aug 17 2019
(GAP) List([1..20], n-> 5^(n-1)*Product([0..n-1], k-> 5*k+1)/Factorial(n)); # G. C. Greubel, Aug 17 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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