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 A001046 a(n) = n*(n-1)*a(n-1)/2 + a(n-2), a(0) = a(1) = 1. (Formerly M1811 N0717) 3
 1, 1, 2, 7, 44, 447, 6749, 142176, 3987677, 143698548, 6470422337, 356016927083, 23503587609815, 1833635850492653, 166884365982441238, 17524692064006822643, 2103129932046801158398, 286043195450428964364771, 43766712033847678348968361 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES 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 T. D. Noe, Table of n, a(n) for n = 0..100 R. K. Guy, Letters to N. J. A. Sloane, June-August 1968 EXAMPLE a(4) = 4*3*7/2 + 2 = 44. MAPLE a := proc (n) option remember; if n < 2 then 1 else binomial(n, 2)*a(n-1)+a(n-2) fi; end proc; seq(a(n), n = 0..20); # G. C. Greubel, Sep 20 2019 MATHEMATICA RecurrenceTable[{a[0]==a[1]==1, a[n]==n(n-1) a[n-1]/2+a[n-2]}, a[n], {n, 20}] (* Harvey P. Dale, Sep 07 2011 *) t = {1, 1}; Do[AppendTo[t, n*(n-1)*t[[-1]]/2 + t[[-2]]], {n, 2, 20}] (* T. D. Noe, Jun 25 2012 *) PROG (PARI) m=20; v=concat([1, 1], vector(m-2)); for(n=3, m, v[n]=binomial(n-1, 2)*v[n-1] + v[n-2] ); v \\ G. C. Greubel, Sep 20 2019 (Magma) I:=[1, 1]; [n le 2 select I[n] else Binomial(n-1, 2)*Self(n-1) + Self(n-2): n in [1..20]]; // G. C. Greubel, Sep 20 2019 (Sage) def a(n): if (n<2): return 1 else: return binomial(n, 2)*a(n-1)+a(n-2) [a(n) for n in (0..20)] # G. C. Greubel, Sep 20 2019 (GAP) a:=[1, 1];; for n in [3..20] do a[n]:=Binomial(n-1, 2)*a[n-1]+a[n-2]; od; a; # G. C. Greubel, Sep 20 2019 CROSSREFS Cf. A001052. Sequence in context: A194453 A346258 A242105 * A158257 A348857 A172389 Adjacent sequences: A001043 A001044 A001045 * A001047 A001048 A001049 KEYWORD nonn,easy AUTHOR N. J. A. Sloane EXTENSIONS More terms from James A. Sellers, Oct 05 2000 STATUS approved

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Last modified April 14 05:31 EDT 2024. Contains 371655 sequences. (Running on oeis4.)