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 A000910 a(n) = 5*binomial(n, 6). (Formerly M3973 N1643) 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 (list; graph; refs; listen; history; text; internal format)
 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 STATUS approved

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)