A001052 a(n) = n*(n-1)*a(n-1)/2 + a(n-2), a(0) = 1, a(1) = 2. (Formerly M0911 N0343)

1, 2, 3, 11, 69, 701, 10584, 222965, 6253604, 225352709, 10147125509, 558317255704, 36859086001973, 2875567025409598, 261713458398275391, 27482788698844325653, 3298196357319717353751, 448582187384180404435789, 68636372866136921596029468

Offset

0,2

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

Maple

a := proc (n) option remember;
if n < 2 then n+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

t = {1, 2}; Do[AppendTo[t, n*(n-1)*t[[-1]]/2 + t[[-2]]], {n, 2, 20}] (* T. D. Noe, Jun 25 2012 *)

Prog

(PARI) a(n)=if(n<2, max(0, n+1), n*(n-1)*a(n-1)/2+a(n-2))
(Magma) I:=[1, 2]; [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 n+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, 2];; 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. A001046.

Sequence in context: A065597 A256394 A219513 * A184310 A301347 A241811

Adjacent sequences: A001049 A001050 A001051 * A001053 A001054 A001055

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, Sep 19 2000

Status

approved