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 A013612 #25 Jul 08 2025 02:48:24
%S A013612 1,1,5,1,10,25,1,15,75,125,1,20,150,500,625,1,25,250,1250,3125,3125,1,
%T A013612 30,375,2500,9375,18750,15625,1,35,525,4375,21875,65625,109375,78125,
%U A013612 1,40,700,7000,43750,175000,437500,625000,390625,1,45,900,10500,78750,393750,1312500,2812500,3515625,1953125
%N A013612 Triangle of coefficients in expansion of (1+5x)^n.
%C A013612 Mirror image of A038243. - _Zerinvary Lajos_, Nov 25 2007
%C A013612 T(n,k) equals the number of n-length words on {0,1,...,5} having n-k zeros. - _Milan Janjic_, Jul 24 2015
%H A013612 Alois P. Heinz, <a href="/A013612/b013612.txt">Rows n = 0..140, flattened</a>
%F A013612 G.f.: 1 / [1 - x(1+5y)].
%F A013612 T(n,k) = 5^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k) *C(n,i) *4^(n-i). Row sums are 6^n = A000400(n). - _Mircea Merca_, Apr 28 2012
%p A013612 T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+5*x)^n):
%p A013612 seq(T(n), n=0..10); # _Alois P. Heinz_, Jun 10 2014
%t A013612 row[n_] := CoefficientList[(1 + 5x)^n, x]; Table[row[n], {n, 0, 9}] // Flatten (* _Jean-François Alcover_, Feb 13 2016 *)
%K A013612 tabl,nonn,easy
%O A013612 0,3
%A A013612 _N. J. A. Sloane_