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 A362288 a(n) = Product_{k=0..n} binomial(n,k)^k. 5
 1, 1, 2, 27, 9216, 312500000, 4251528000000000, 95432797246104853383515625, 14719075154533285649961930052505436160000, 65577306173662530591576256095315195684570038194755952705536 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Winston de Greef, Table of n, a(n) for n = 0..22 FORMULA a(n) = Product_{k=0..n} n!^k / k!^n. a(n) = A067055(n) / A255268(n). a(n) ~ A^n * exp((6*n^3 + 12*n^2 - n - 1)/24) / ((2*Pi)^(n*(n+1)/4) * n^(n*(3*n+2)/12)), where A is the Glaisher-Kinkelin constant A074962. MATHEMATICA Table[Product[Binomial[n, k]^k, {k, 0, n}], {n, 0, 10}] Table[(n!)^(n*(n+1)/2) / BarnesG[n+2]^n, {n, 0, 10}] PROG (PARI) a(n) = prod(k=0, n, binomial(n, k)^k); \\ Michel Marcus, Apr 14 2023 CROSSREFS Cf. A001142, A067055, A167008, A255268, A272093. Sequence in context: A299116 A076113 A182335 * A056013 A363403 A007257 Adjacent sequences: A362285 A362286 A362287 * A362289 A362290 A362291 KEYWORD nonn AUTHOR Vaclav Kotesovec, Apr 14 2023 STATUS approved

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Last modified September 8 15:42 EDT 2024. Contains 375753 sequences. (Running on oeis4.)