%I #15 Oct 01 2023 12:10:36

%S 1,15,175,1750,15750,131250,1031250,7734375,55859375,391015625,

%T 2666015625,17773437500,116210937500,747070312500,4731445312500,

%U 29571533203125,182647705078125,1116180419921875,6755828857421875

%N Expansion of (-1+1/(1-5*x)^5)/(25*x); related to A036071.

%H W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">On generalizations of Stirling number triangles</a>, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (25, -250, 1250, -3125, 3125).

%F a(n) = 5^(n-1)*binomial(n+5, 4);

%F g.f. (-1+(1-5*x)^(-5))/(x*5^2).

%o (Sage)[lucas_number2(n, 5, 0)*binomial(n,4)/5^6 for n in range(5, 24)] # _Zerinvary Lajos_, Mar 13 2009

%Y Cf. A036070, A036071. a(n)= A030527(n+1, 1) (first column of triangle).

%K easy,nonn

%O 0,2

%A _Wolfdieter Lang_