A016297 Expansion of 1/((1-2*x) * (1-5*x) * (1-8*x)).

1, 15, 159, 1475, 12831, 107835, 888679, 7239555, 58567311, 471793355, 3790622199, 30406356435, 243657749791, 1951296498075, 15620544499719, 125015218606115, 1000376061956271, 8004280061317995, 64040598319145239, 512356575696692595, 4099011551292242751

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (15,-66,80).

Formula

From Vincenzo Librandi, Mar 16 2011: (Start)

a(n) = 15*a(n-1) - 66*a(n-2) + 80*a(n-3), n >= 3.

a(n) = 13*a(n-1) - 40*a(n-2) + 2^n, n >= 2. (End)

a(n) = 4*8^(n+1)/9 + 2^(n+1)/9 - 5^(n+2)/9. - R. J. Mathar, Mar 18 2011

From Seiichi Manyama, May 04 2025: (Start)

a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2).

a(n) = Sum_{k=0..n} (-3)^k * 8^(n-k) * binomial(n+2,k+2) * Stirling2(k+2,2). (End)

E.g.f.: exp(2*x)*(2 - 25*exp(3*x) + 32*exp(6*x))/9. - Stefano Spezia, May 04 2025

Mathematica

LinearRecurrence[{15, -66, 80}, {1, 15, 159}, 25] (* Paolo Xausa, May 10 2026 *)

Crossrefs

Cf. A016127, A025999.

Sequence in context: A183555 A232415 A395783 * A206811 A027544 A021048

Adjacent sequences: A016294 A016295 A016296 * A016298 A016299 A016300

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved