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

0,2

Links

Table of n, a(n) for n=0..18.

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).

Formula

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

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A082678 A331516 A107395 * A346320 A051588 A016164

Adjacent sequences: A036080 A036081 A036082 * A036084 A036085 A036086

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved