

A057527


4th level factorials: product of first n superduperfactorials.


4




OFFSET

0,3


COMMENTS

In general for kth level factorials a(n) =Product of first n (k1)th level factorials =Product[i^C(ni+k1,ni)] over 1<=i<=n.


LINKS

Table of n, a(n) for n=0..7.


FORMULA

a(n) =a(n1)*A055462(n) =Product[i^A000332(ni)] over 1<=i<=n.
a(n) ~ exp(11/72  5*n/6  4*n^2/3  11*n^3/18  25*n^4/288 + Zeta(3)*(n+2) / (8*Pi^2) + Zeta'(3)/6) * n^(251/720 + n + 11*n^2/12 + n^3/3 + n^4/24) * (2*Pi)^((n+1)*(n+2)*(n+3)/12) / A^(11/6 + 2*n + n^2/2), where Zeta(3) = A002117, Zeta'(3) = A259068 = 0.0053785763577743011444169742104138428956644397... and A = A074962 = 1.28242712910062263687534256886979... is the GlaisherKinkelin constant.  Vaclav Kotesovec, Jul 24 2015


EXAMPLE

a(4) =((4!*3!*2!*1!)*(3!*2!*1!)*(2!*1!)*(1!)) * ((3!*2!*1!)*(2!*1!)*(1!)) * ((2!*1!)*(1!)) * ((1!)) =24*6^3*2^6*1^10 =331776


MATHEMATICA

Table[Product[i^Binomial[ni+3, 3], {i, 1, n}], {n, 0, 10}] (* Vaclav Kotesovec, Jul 24 2015 *)


CROSSREFS

Cf. A000142, A000178, A055462, A057528, A260404 for first, second, third, fifth and sixth level factorials.
Sequence in context: A203305 A191954 A212170 * A166475 A152688 A046873
Adjacent sequences: A057524 A057525 A057526 * A057528 A057529 A057530


KEYWORD

easy,nonn


AUTHOR

Henry Bottomley, Sep 02 2000


STATUS

approved



