A000910 a(n) = 5*binomial(n, 6).

0, 0, 0, 0, 0, 0, 5, 35, 140, 420, 1050, 2310, 4620, 8580, 15015, 25025, 40040, 61880, 92820, 135660, 193800, 271320, 373065, 504735, 672980, 885500, 1151150, 1480050, 1883700, 2375100, 2968875, 3681405, 4530960, 5537840, 6724520, 8115800, 9738960, 11623920, 13803405

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• Charles Jordan, Calculus of Finite Differences, Budapest, 1939, p. 449.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

A diagonal of A088617.

Cf. A080159, A000579, A210569.

Programs

Mathematica

Table[5Binomial[n, 6], {n, 0, 100}] (* Stefan Steinerberger, Apr 30 2006 *)

PARI

a(n)=5*binomial(n,6) \\ Charles R Greathouse IV, Oct 07 2015

SageMath

[5*binomial(n,6) for n in (0..40)] # G. C. Greubel, May 22 2022

Formula

a(n) = 5*A000579(n+3) = A080159(n+3, 3).

G.f.: 5*x^6/(1-x)^7. - Colin Barker, Mar 01 2012

E.g.f.: x^6*exp(x)/144. - G. C. Greubel, May 22 2022

From Amiram Eldar, Jul 19 2022: (Start)

Sum_{n>=6} 1/a(n) = 6/25.

Sum_{n>=6} (-1)^n/a(n) = 192*log(2)/5 - 661/25. (End)