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
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..50
Programs
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Maple
a:= n-> sum(binomial(n+2*j-1, 2*j), j=0..2^n-1): seq(a(n), n=0..20);
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Mathematica
Table[Sum[Binomial[n+2*j-1,2*j],{j,0,2^n-1}],{n,0,15}] (* Vaclav Kotesovec, Sep 22 2013 *)
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