A000910 a(n) = 5*binomial(n, 6). (Formerly M3973 N1643)

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

0,7

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).

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)

Mathematica

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

Prog

(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

Crossrefs

A diagonal of A088617.

Cf. A080159, A000579, A210569.

Sequence in context: A053126 A096743 A026697 * A005562 A097872 A184707

Adjacent sequences: A000907 A000908 A000909 * A000911 A000912 A000913

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved