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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Crossrefs

Cf. A001046.

Programs

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

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

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 *)

PARI

a(n)=if(n<2,max(0,n+1),n*(n-1)*a(n-1)/2+a(n-2))

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

Extensions

More terms from James Sellers, Sep 19 2000