A260404 6th level factorials: product of first n 5th level factorials.

1, 1, 2, 192, 6115295232, 15436756676507918107049554083840, 18356962141505758798331790171539976807981714702571497465907439808868887035904000000

Offset

0,3

Comments

In general for k-th level factorials a(n) = Product_{j=1..n} j^C(n-j+k-1,k-1).

Links

Table of n, a(n) for n=0..6.

Formula

a(n) ~ exp(137/720 - 11*n/16 - 737*n^2/480 - 53*n^3/48 - 421*n^4/1152 - 137*n^5/2400 - 49*n^6/14400 + (3 + n)*(15 + 12*n + 2*n^2)*Zeta(3)/(96*Pi^2) - (3 + n)*Zeta(5) / (32*Pi^4) + (17 + 12*n + 2*n^2)*Zeta'(-3)/24 + Zeta'(-5)/120) * n^(19087/60480 + n + 137*n^2/120 + 5*n^3/8 + 17*n^4/96 + n^5/40 + n^6/720) * (2*Pi)^((n+1)*(n+2)*(n+3)*(n+4)*(n+5)/240) / A^(137/60 + 15*n/4 + 17*n^2/8 + n^3/2 + n^4/24), where Zeta(3) = A002117, Zeta(5) = A013663, Zeta'(-3) = A259068, Zeta'(-5) = A259070 and A = A074962 is the Glaisher-Kinkelin constant.

Mathematica

Table[Product[i^Binomial[n-i+5, 5], {i, 1, n}], {n, 0, 10}]

Crossrefs

Cf. A000142, A000178, A055462, A057527, A057528.

Sequence in context: A151709 A265750 A174827 * A064682 A139949 A229017

Adjacent sequences: A260401 A260402 A260403 * A260405 A260406 A260407

Keyword

nonn

Author

Vaclav Kotesovec, Jul 24 2015

Status

approved