A036070 Expansion of (-1+1/(1-4*x)^4)/(16*x); related to A038846.

1, 10, 80, 560, 3584, 21504, 122880, 675840, 3604480, 18743296, 95420416, 477102080, 2348810240, 11408506880, 54760833024, 260113956864, 1224065679360, 5712306503680, 26456998543360, 121702193299456, 556352883654656, 2528876743884800, 11434920928870400, 51457144179916800

Offset

0,2

Links

Table of n, a(n) for n=0..23.

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 (16,-96,256,-256).

Formula

a(n) = A030526(n+1, 1).

a(n) = 4^(n-1)*binomial(n+4, 3).

G.f.: (-1+(1-4*x)^(-4))/(x*4^2).

From Amiram Eldar, Nov 03 2025: (Start)

Sum_{n>=0} 1/a(n) = 1728*log(4/3) - 496.

Sum_{n>=0} (-1)^n/a(n) = 1072 - 4800*log(5/4). (End)

Mathematica

a[n_] := 4^(n-1) * Binomial[n+4, 3]; Array[a, 24, 0] (* Amiram Eldar, Nov 03 2025 *)

Crossrefs

First column of triangle A030526.

Cf. A038846, A001787.

Sequence in context: A000575 A220485 A055285 * A374511 A377199 A257286

Adjacent sequences: A036067 A036068 A036069 * A036071 A036072 A036073

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved