A053111 Expansion of (-1 + 1/(1-8*x)^8)/(64*x); related to A053107.

1, 36, 960, 21120, 405504, 7028736, 112459776, 1686896640, 23991418880, 326283296768, 4271344975872, 54103703027712, 665891729571840, 7990700754862080, 93757555523715072, 1078211888522723328, 12177451917433110528, 135305021304812339200, 1481233917442156134400

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (64,-1792,28672,-286720,1835008,-7340032,16777216,-16777216).

Formula

a(n) = 8^(n-1)*binomial(n+8, 7).

G.f.: (-1 + (1-8*x)^(-8))/(x*8^2).

From Amiram Eldar, Nov 03 2025: (Start)

Sum_{n>=0} 1/a(n) = 421654016*log(8/7) - 844560704/15.

Sum_{n>=0} (-1)^n/a(n) = 3365092928/15 - 1904684544*log(9/8). (End)

Mathematica

Table[8^(n - 1)*Binomial[n + 8, 7], {n, 0, 30}] (* G. C. Greubel, Aug 16 2018 *)
CoefficientList[Series[(-1+1/(1-8x)^8)/(64x), {x, 0, 20}], x] (* Harvey P. Dale, Jun 20 2021 *)

Prog

(PARI) vector(30, n, n--; 8^(n-1)*binomial(n+8, 7)) \\ G. C. Greubel, Aug 16 2018
(Magma) [8^(n-1)*Binomial(n+8, 7): n in [0..30]]; // G. C. Greubel, Aug 16 2018

Crossrefs

Cf. A053107, A053110, A053112, A053113.

Sequence in context: A167250 A218177 A107398 * A260855 A130563 A240685

Adjacent sequences: A053108 A053109 A053110 * A053112 A053113 A053114

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved