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.
%I A018901 #30 Mar 19 2025 08:04:25
%S A018901 1,1,6,27,146,780,4332,24017,135954,767394,4395456,25090131,144840476,
%T A018901 833196442,4836766584,27981391815,163112472594,947712321234,
%U A018901 5542414273884,32312202610863,189456975899496,1107575676600876
%N A018901 Central hexanomial coefficients: largest coefficient of (1 + x + ... + x^5)^n.
%C A018901 Greatest multiplicity of one- or two-dimensional standard representation of Lie algebras sl(2) in decomposition of tensor power F6^k, where F6 is the standard 6-dimensional irreducible representation of sl(2). - _Leonid Bedratyuk_, Jul 22 2004
%C A018901 Sum_{k=0..floor(5*n/12)} (-1)^k*binomial(n,k)*binomial(n + floor(5*n/2) - 6*k - 1, n-1). - _Warut Roonguthai_, May 21 2006
%H A018901 T. D. Noe, <a href="/A018901/b018901.txt">Table of n, a(n) for n = 0..200</a>
%H A018901 Vaclav Kotesovec, <a href="/A018901/a018901.txt">Recurrence</a>
%H A018901 <a href="/index/Ce#cfn">Index entries for sequences of k-nomial coefficients</a>
%F A018901 a(n) ~ 6^n * sqrt(6/(35*Pi*n)). - _Vaclav Kotesovec_, Aug 09 2013
%e A018901 Number of ways of getting most likely sum using n 6-sided dice (e.g., for n=2, 7 is the most prevalent sum and there are 6 different ways to get it: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1).
%p A018901 sum((-1)^(k)*binomial(n,k)*binomial(n+floor(5*n/2)-6*k-1, n-1), k=0..floor(5*n/12)); # _Warut Roonguthai_, May 21 2006
%t A018901 Flatten[{1,Table[Coefficient[Expand[Sum[x^j,{j,0,5}]^n],x^Floor[5*n/2]],{n,1,20}]}] (* _Vaclav Kotesovec_, Aug 09 2013 *)
%Y A018901 Cf. A063419 (bisection). Row 6 of A077042.
%K A018901 nonn
%O A018901 0,3
%A A018901 Jonn Dalton jdalton(AT)vnet.ibm.com