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

%I #20 Sep 22 2013 20:40:32

%S 1,2,16,372,24616,5014592,3349471840,7649590386464,61356625102897216,

%T 1758844330913892684288,182379122144778004351027200,

%U 69026760045145802122822210022400,96048744530120196897251255933762037760,494360393380904255996973467025921794482614272

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

%H Alois P. Heinz, <a href="/A227406/b227406.txt">Table of n, a(n) for n = 0..50</a>

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

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

%F a(n) ~ 2^(n^2+n-1)/n!. - _Vaclav Kotesovec_, Sep 22 2013

%p a:= n-> sum(binomial(n+2*j-1, 2*j), j=0..2^n-1):

%p seq(a(n), n=0..20);

%t Table[Sum[Binomial[n+2*j-1,2*j],{j,0,2^n-1}],{n,0,15}] (* _Vaclav Kotesovec_, Sep 22 2013 *)

%Y Cf. A071920, A227402.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Sep 21 2013

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)