A036083 Expansion of (-1+1/(1-5*x)^5)/(25*x); related to A036071.

1, 15, 175, 1750, 15750, 131250, 1031250, 7734375, 55859375, 391015625, 2666015625, 17773437500, 116210937500, 747070312500, 4731445312500, 29571533203125, 182647705078125, 1116180419921875, 6755828857421875

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
• Index entries for linear recurrences with constant coefficients, signature (25, -250, 1250, -3125, 3125).

Crossrefs

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

Programs

Mathematica

LinearRecurrence[{25,-250,1250,-3125,3125},{1,15,175,1750,15750},20] (* Harvey P. Dale, Aug 29 2024 *)

Sage

[lucas_number2(n, 5, 0)*binomial(n,4)/5^6 for n in range(5, 24)] # Zerinvary Lajos, Mar 13 2009

Formula

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

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