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A227402 Number of unimodal functions f:[n]->[n^2]. 4

%I #18 Aug 29 2014 10:40:39

%S 1,1,16,525,24616,1505205,113772114,10253539205,1073769343504,

%T 128165285630637,17177527372642000,2554518029816653175,

%U 417444979902876203656,74358489250362053975095,14340040595865309129453250,2976703788777987140216622005

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

%H Alois P. Heinz, <a href="/A227402/b227402.txt">Table of n, a(n) for n = 0..110</a>

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

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

%F a(n) ~ 2^(n-3/2) * n^(n-1/2) * exp(n+1/4) / sqrt(Pi). - _Vaclav Kotesovec_, Aug 29 2014

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

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

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

%Y Main diagonal of A226031.

%Y Cf. A071920, A227406.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 20 2013

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)