cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A086687 a(n) = binomial(n!,n).

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%I A086687 #17 May 12 2025 11:53:46
%S A086687 1,1,1,20,10626,190578024,189492294437160,16321981448897949868560,
%T A086687 173117930575796585984663510371920,
%U A086687 300649979042426162195454856425990347600496000,109109335363647915965076917082046041529603540914857910625920
%N A086687 a(n) = binomial(n!,n).
%H A086687 Alois P. Heinz, <a href="/A086687/b086687.txt">Table of n, a(n) for n = 0..30</a>
%H A086687 Harlan J. Brothers, <a href="https://doi.org/10.35834/2025/3701067">Pascal's triangle, Sidi polynomials, and powers of e</a>, Missouri J. Math. Sci. (2025) Vol. 37, No. 1, 67-78.
%F A086687 From _Vaclav Kotesovec_, Jul 02 2016: (Start)
%F A086687 a(n) ~ (n!)^(n-1).
%F A086687 a(n) ~ 2^((n-1)/2) * Pi^((n-1)/2) * n^((2*n+1)*(n-1)/2) / exp(n^2-n-1/12).
%F A086687 (End)
%t A086687 Table[Binomial[n!,n],{n,0,12}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 03 2011*)
%o A086687 (PARI) for(i=1,10,print1(","binomial(i!,i)))
%Y A086687 Cf. A036740.
%Y A086687 Main diagonal of A180397.
%K A086687 nonn
%O A086687 0,4
%A A086687 _Jon Perry_, Jul 28 2003
%E A086687 a(0)=1 prepended by _Alois P. Heinz_, Nov 06 2016