A227406 Number of unimodal functions f:[n]->[2^n].

1, 2, 16, 372, 24616, 5014592, 3349471840, 7649590386464, 61356625102897216, 1758844330913892684288, 182379122144778004351027200, 69026760045145802122822210022400, 96048744530120196897251255933762037760, 494360393380904255996973467025921794482614272

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..50

Formula

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

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

a(n) ~ 2^(n^2+n-1)/n!. - Vaclav Kotesovec, Sep 22 2013

Maple

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

Mathematica

Table[Sum[Binomial[n+2*j-1, 2*j], {j, 0, 2^n-1}], {n, 0, 15}] (* Vaclav Kotesovec, Sep 22 2013 *)

Crossrefs

Cf. A071920, A227402.

Sequence in context: A009341 A366396 A015201 * A068471 A325287 A140308

Adjacent sequences: A227403 A227404 A227405 * A227407 A227408 A227409

Keyword

nonn

Author

Alois P. Heinz, Sep 21 2013

Status

approved