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.

A025037 Number of partitions of { 1, 2, ..., 5n } into sets of size 5.

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%I A025037 #43 Aug 28 2025 10:28:45
%S A025037 1,1,126,126126,488864376,5194672859376,123378675083039376,
%T A025037 5721809435651034101376,470624547891733205872277376,
%U A025037 63887753000850674430367526069376,13536281554808237495608549953475109376,4280862577989659916223699531336456815269376
%N A025037 Number of partitions of { 1, 2, ..., 5n } into sets of size 5.
%H A025037 Vincenzo Librandi, <a href="/A025037/b025037.txt">Table of n, a(n) for n = 0..100</a> (term a(0) added by Sidney Cadot)
%H A025037 Cyril Banderier, Philippe Marchal, and Michael Wallner, <a href="https://arxiv.org/abs/1805.09017">Rectangular Young tableaux with local decreases and the density method for uniform random generation</a> (short version), arXiv:1805.09017 [cs.DM], 2018.
%H A025037 Robert Coquereaux and Jean-Bernard Zuber, <a href="https://arxiv.org/abs/2305.01100">Counting partitions by genus. II. A compendium of results</a>, arXiv:2305.01100 [math.CO], 2023. See p. 17.
%F A025037 a(n) = (5n)!/(n!(5!)^n). - _Christian G. Bower_, Sep 15 1998
%F A025037 a(n) ~ 5^(4*n+1/2) * (n/e)^(4*n) / 24^n. - _Amiram Eldar_, Aug 28 2025
%t A025037 Table[(5n)!/(n!(5!)^n),{n,0,10}] (* _Vincenzo Librandi_, Jun 26 2012 *)
%o A025037 (Sage) [rising_factorial(n+1,4*n)/120^n for n in (0..15)] # _Peter Luschny_, Jun 26 2012
%o A025037 (Magma) [Factorial(5*n)/(Factorial(n)*Factorial(5)^n): n in [0..10]]; // _Vincenzo Librandi_, Jun 26 2012
%Y A025037 Column k=5 of A060540.
%K A025037 nonn,changed
%O A025037 0,3
%A A025037 _David W. Wilson_
%E A025037 a(0) from _Peter Luschny_, Apr 24 2023