A227402 Number of unimodal functions f:[n]->[n^2].

1, 1, 16, 525, 24616, 1505205, 113772114, 10253539205, 1073769343504, 128165285630637, 17177527372642000, 2554518029816653175, 417444979902876203656, 74358489250362053975095, 14340040595865309129453250, 2976703788777987140216622005

Offset: 0

Author

Alois P. Heinz, Sep 20 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..110

Crossrefs

Main diagonal of A226031.

Cf. A071920, A227406.

Programs

Maple

a:= n-> `if`(n=0, 1, add(binomial(n+2*j-1, 2*j), j=0..n^2-1)):
seq(a(n), n=0..20);

Mathematica

Flatten[{1,Table[Sum[Binomial[n+2*j-1, 2*j], {j,0,n^2-1}],{n,1,20}]}] (* Vaclav Kotesovec, Aug 29 2014 *)

Formula

a(n) = Sum_{j=0..n^2-1} C(n+2*j-1,2*j), a(0) = 1.

a(n) = A071921(n,n^2).

a(n) ~ 2^(n-3/2) * n^(n-1/2) * exp(n+1/4) / sqrt(Pi). - Vaclav Kotesovec, Aug 29 2014