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%I M3973 N1643 #42 Jul 19 2022 05:46:36
%S 0,0,0,0,0,0,5,35,140,420,1050,2310,4620,8580,15015,25025,40040,61880,
%T 92820,135660,193800,271320,373065,504735,672980,885500,1151150,
%U 1480050,1883700,2375100,2968875,3681405,4530960,5537840,6724520,8115800,9738960,11623920,13803405
%N a(n) = 5*binomial(n, 6).
%D Charles Jordan, Calculus of Finite Differences, Budapest, 1939, p. 449.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A000910/b000910.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F a(n) = 5*A000579(n+3) = A080159(n+3, 3).
%F G.f.: 5*x^6/(1-x)^7. - _Colin Barker_, Mar 01 2012
%F E.g.f.: x^6*exp(x)/144. - _G. C. Greubel_, May 22 2022
%F From _Amiram Eldar_, Jul 19 2022: (Start)
%F Sum_{n>=6} 1/a(n) = 6/25.
%F Sum_{n>=6} (-1)^n/a(n) = 192*log(2)/5 - 661/25. (End)
%t Table[5Binomial[n, 6], {n, 0, 100}] (* _Stefan Steinerberger_, Apr 30 2006 *)
%o (PARI) a(n)=5*binomial(n,6) \\ _Charles R Greathouse IV_, Oct 07 2015
%o (SageMath) [5*binomial(n,6) for n in (0..40)] # _G. C. Greubel_, May 22 2022
%Y A diagonal of A088617.
%Y Cf. A080159, A000579, A210569.
%K nonn,easy
%O 0,7
%A _N. J. A. Sloane_
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