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, 40534973144531250, 241279602050781250, 1425743103027343750

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Wolfdieter Lang, On generalizations of the Stirling number triangles, J. Integer Seq., Vol. 3 (2000), Article 00.2.4.

Index entries for linear recurrences with constant coefficients, signature (25,-250,1250,-3125,3125).

Formula

a(n) = A030527(n+1, 1).

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

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

From Amiram Eldar, Nov 03 2025: (Start)

Sum_{n>=0} 1/a(n) = 21425/3 - 32000*log(5/4).

Sum_{n>=0} (-1)^n/a(n) = 59075/3 - 108000*log(6/5). (End)

Mathematica

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

Prog

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

Crossrefs

First column of triangle A030527.

Cf. A036070, A036071.

Sequence in context: A331516 A387369 A107395 * A346320 A051588 A016164

Adjacent sequences: A036080 A036081 A036082 * A036084 A036085 A036086

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved