A088625 a(n) = 14*binomial(n,8). (Formerly N2116)

0, 0, 0, 0, 0, 0, 0, 0, 14, 126, 630, 2310, 6930, 18018, 42042, 90090, 180180, 340340, 612612, 1058148, 1763580, 2848860, 4476780, 6864396, 10296594, 15142050, 21871850, 31081050, 43513470, 60090030, 81940950, 110442150, 147256200, 194378184, 254186856, 329501480

Offset

0,9

References

Charles Jordan, Calculus of Finite Differences, Chelsea, 1965, p. 449.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Links

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

G.f.: 14*x^8 / (1-x)^9. - Colin Barker, Dec 19 2012

From Amiram Eldar, Sep 28 2025: (Start)

Sum_{n>=8} 1/a(n) = 4/49.

Sum_{n>=8} (-1)^n/a(n) = 512*log(2)/7 - 37216/735. (End)

Mathematica

a[n_] := 14 * Binomial[n, 8]; Array[a, 40, 0] (* Amiram Eldar, Sep 28 2025 *)

Crossrefs

A diagonal of A088617.

Sequence in context: A025211 A026870 A090296 * A073393 A020918 A275559

Adjacent sequences: A088622 A088623 A088624 * A088626 A088627 A088628

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Revised Nov 23 2003, Jun 12 2012

Status

approved