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%I #23 Apr 14 2021 11:03:15
%S 1,1,6,93,2380,85405,3956106,224939113,15175702200,1185580310121,
%T 105302043709390,10482085765658661,1156062800841590148,
%U 139945327558704629221,18449221488652046992914,2631255715262150125502865,403689862107153669227378416,66297391981691913179574751633
%N a(n) = (1/n) * Sum_{i=0..n-1} C(n,i)*C(n,i+1)*(n-1)^i*n^(n-i) for n>=1, a(0)=1.
%H Andrew Howroyd, <a href="/A103212/b103212.txt">Table of n, a(n) for n = 0..200</a>
%F a(n) = A103209(n, n-1). [corrected by _Vaclav Kotesovec_, Sep 24 2017]
%F a(n) ~ 2^(2*n) * n^(n-3/2) / (sqrt(Pi) * exp(1/2)). - _Vaclav Kotesovec_, Sep 24 2017
%t Table[HypergeometricPFQ[{-n, n+1}, {2}, -n+1], {n, 0, 20}] (* _Vaclav Kotesovec_, Sep 24 2017 *)
%t Flatten[{1, 1, Table[Sum[Binomial[n, k]*Binomial[n, k+1]*(n-1)^k*n^(n-k), {k, 0, n-1}]/n, {n, 2, 20}]}] (* _Vaclav Kotesovec_, Sep 24 2017 *)
%o (PARI) a(n) = {if(n==0, 1, sum(i=0, n-1, binomial(n,i)*binomial(n,i+1)*(n-1)^i*n^(n-i))/n)} \\ _Andrew Howroyd_, Apr 14 2021
%Y Cf. A103209, A292798.
%K nonn
%O 0,3
%A _Ralf Stephan_, Jan 27 2005
%E Prepended a(0)=1 from _Vaclav Kotesovec_, Sep 24 2017
%E Terms a(15) and beyond from _Andrew Howroyd_, Apr 14 2021
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