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A203474 a(n) = A203472(n) / A000178(n-1), where A000178 are the superfactorials. 3
1, 7, 252, 41580, 29729700, 89278289100, 1104908105901600, 55674109640169820800, 11329124570678156834592000, 9258047307912482983660236480000, 30262334718212007877669234596364800000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..11.

FORMULA

a(n) ~ 3*A^(3/2) * 2^(n^2 + 4*n + 185/24) * exp(n/2 - 1/8) / (Pi^(n/2 + 3/2) * n^(n/2 + 59/8)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Apr 09 2021

MATHEMATICA

f[j_] := j + 2; z = 16;

v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]

d[n_] := Product[(i - 1)!, {i, 1, n}] (* A000178(n-1) *)

Table[v[n], {n, 1, z}] (* A203472 *)

Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203473 *)

Table[v[n]/d[n], {n, 1, 20}] (* A203474 *)

CROSSREFS

Cf. A203472, A203473, A093883.

Sequence in context: A347843 A338633 A142805 * A228291 A119942 A188421

Adjacent sequences: A203471 A203472 A203473 * A203475 A203476 A203477

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jan 02 2012

EXTENSIONS

Definition corrected by Vaclav Kotesovec, Apr 09 2021

STATUS

approved

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Last modified November 30 04:37 EST 2022. Contains 358431 sequences. (Running on oeis4.)