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A000910
a(n) = 5*binomial(n, 6).
(Formerly M3973 N1643)
7
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).
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.
Sequence in context: A053126 A096743 A026697 * A005562 A097872 A184707
KEYWORD
nonn,easy
STATUS
approved