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 A025015 #32 Mar 19 2025 08:06:17
%S A025015 1,1,10,75,670,6000,55252,512365,4816030,45433800,432457640,
%T A025015 4123838279,39581170420,380242296850,3671331273480,35460394945125,
%U A025015 343900019857310,3335361909606710,32458256583753952,315825118347405835
%N A025015 Central decanomial coefficients: largest coefficient of (1 + x + ... + x^9)^n.
%C A025015 Number of integers in [0, 10^n-1] whose sums of digits are equal to the most common value, which is 9*n/2 for even n and (9*n +/- 1)/2 for odd n > 1. E.g., the most common value of sums of digits of numbers from 0 to 9999 is 9*4/2 = 18, so there are a(4)=670 numbers in this range whose sums of digits are 18. - _Warut Roonguthai_, Jun 08 2006
%C A025015 Generally, largest coefficient of (1 + x + ... + x^k)^n is asymptotic to (k+1)^n * sqrt(6/(k*(k+2)*Pi*n)). - _Vaclav Kotesovec_, Aug 09 2013
%C A025015 a(n) is the largest coefficients of the n-th row of A213651. - _Miquel Cerda_, Jul 19 2017
%H A025015 T. D. Noe, <a href="/A025015/b025015.txt">Table of n, a(n) for n=0..200</a>
%H A025015 Vaclav Kotesovec, <a href="/A025015/a025015.txt">Recurrence</a>
%H A025015 <a href="/index/Ce#cfn">Index entries for sequences of k-nomial coefficients</a>
%F A025015 a(n) = Sum_{k=0..floor(9*n/20)}(-1)^(k)*binomial(n, k)*binomial(n+floor(9*n/2)-10*k-1, n-1). - _Warut Roonguthai_, Jun 08 2006
%F A025015 a(n) ~ 10^n * sqrt(2/(33*Pi*n)). - _Vaclav Kotesovec_, Aug 09 2013
%t A025015 Flatten[{1,Table[Coefficient[Expand[Sum[x^j,{j,0,9}]^n],x^Floor[9*n/2]],{n,1,20}]}] (* _Vaclav Kotesovec_, Aug 09 2013 *)
%Y A025015 Row 10 of A077042.
%K A025015 easy,nonn
%O A025015 0,3
%A A025015 _David W. Wilson_