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 A263430 a(n) = Product_{k=0..n} (4*k+1)^(n-k). 1
 1, 1, 5, 225, 131625, 1309010625, 273380323978125, 1427352844030287890625, 216119240915841469025244140625, 1079864992142473709995957417730712890625, 199639840782299404795675492100337942688751220703125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS G. C. Greubel, Table of n, a(n) for n = 0..36 Eric Weisstein's World of Mathematics, Catalan's Constant Eric Weisstein's World of Mathematics, Glaisher-Kinkelin Constant FORMULA a(n) ~ A^(1/8) * 2^(n^2 + 3*n/2 + 1/8) * Pi^(n/2 + 1/8) * n^(n^2/2 + n/4 - 5/96) / (Gamma(1/4)^(n + 1/4) * exp(3*n^2/4 + n/4 + 1/96 - C/(4*Pi))), where A = A074962 is the Glaisher-Kinkelin constant and C = A006752 = is Catalan's constant. MATHEMATICA Table[Product[(4*k+1)^(n-k), {k, 0, n}], {n, 0, 10}] PROG (PARI) for(n=0, 10, print1(prod(k=0, n, (4*k+1)^(n-k)), ", ")) \\ G. C. Greubel, Aug 25 2018 (Magma) [(&*[(4*k+1)^(n-k): k in [0..n]]): n in [0..10]]; // G. C. Greubel, Aug 25 2018 CROSSREFS Cf. A000178, A057863, A263416. Sequence in context: A225818 A185551 A324098 * A339311 A200988 A201491 Adjacent sequences: A263427 A263428 A263429 * A263431 A263432 A263433 KEYWORD nonn AUTHOR Vaclav Kotesovec, Oct 18 2015 STATUS approved

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Last modified August 3 21:27 EDT 2024. Contains 374905 sequences. (Running on oeis4.)