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 A034688 Expansion of (1-25*x)^(-1/5), related to quintic factorial numbers A008548. 10
 1, 5, 75, 1375, 27500, 577500, 12512500, 277062500, 6233906250, 141994531250, 3265874218750, 75708902343750, 1766541054687500, 41445770898437500, 976936028320312500, 23120819336914062500, 549119459251708984375 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..500 A. Straub, V. H. Moll, T. Amdeberhan, The p-adic valuation of k-central binomial coefficients, Acta Arith. 140 (1) (2009) 31-41, eq (1.10) FORMULA a(n) = (5^n/n!)*A008548(n), n >= 1, a(0) := 1, where A008548(n)=(5*n-4)(!^5) := product(5*j-4, j=1..n). G.f.: (1-25*x)^(-1/5). a(n) ~ Gamma(1/5)^-1*n^(-4/5)*5^(2*n)*{1 - 2/25*n^-1 - ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001 a(n) = (-25)^n*binomial(-1/5, n). - Peter Luschny, Oct 23 2018 MAPLE A034688 := n -> (-25)^n*binomial(-1/5, n): seq(A034688(n), n=0..16); # Peter Luschny, Oct 23 2018 CROSSREFS Cf. A008548, A034385, A034687. Sequence in context: A224088 A219462 A091882 * A238608 A132855 A238560 Adjacent sequences:  A034685 A034686 A034687 * A034689 A034690 A034691 KEYWORD easy,nonn AUTHOR STATUS approved

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Last modified February 19 18:51 EST 2019. Contains 320328 sequences. (Running on oeis4.)