A001046 a(n) = n*(n-1)*a(n-1)/2 + a(n-2), a(0) = a(1) = 1. (Formerly M1811 N0717)

1, 1, 2, 7, 44, 447, 6749, 142176, 3987677, 143698548, 6470422337, 356016927083, 23503587609815, 1833635850492653, 166884365982441238, 17524692064006822643, 2103129932046801158398, 286043195450428964364771, 43766712033847678348968361

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