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

%I

%S 1,1,2,192,6115295232,15436756676507918107049554083840,

%T 18356962141505758798331790171539976807981714702571497465907439808868887035904000000

%N 6th level factorials: product of first n 5th level factorials.

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

%F 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.

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

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

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jul 24 2015

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Last modified February 27 09:40 EST 2020. Contains 332301 sequences. (Running on oeis4.)