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A174826 Hankel transform of median Euler numbers A000657. 1
1, 3, 1260, 471517200, 550527639742080000, 5190428913555819988454400000000, 850897011688550259860209488988778496000000000000, 4613713285873452716084822982464795709127827429408768000000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) = Product_{k=0..n} ((k+1)*(4k+1)*(4k+3)*floor((2k+3)/2))^(n-k).
a(n) ~ sqrt(Gamma(1/4)) * 2^(2*n^2 + 7*n/2 + 9/8) * n^(n*(2*n+3) + 47/48) * Pi^(n + 3/4) / (A^(7/4) * exp(3*n*(n+1) - 7/48)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Feb 24 2019
MATHEMATICA
Table[Product[((k+1)*(4*k+1)*(4*k+3)*Floor[(2*k+3)/2])^(n-k), {k, 0, n}], {n, 0, 10}] (* Vaclav Kotesovec, Feb 24 2019 *)
CROSSREFS
Sequence in context: A034315 A172924 A129078 * A122389 A036066 A262516
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 30 2010
EXTENSIONS
a(5) and following corrected by Georg Fischer, Jan 18 2024
STATUS
approved

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Last modified March 29 03:51 EDT 2024. Contains 371264 sequences. (Running on oeis4.)