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%I #21 Aug 11 2015 06:41:25
%S 1,7,39,202,1015,5028,24731,121208,593019,2899335,14173401,69301422,
%T 338990145,1659037695,8124085575,39806373880,195160896835,
%U 957396540285,4699409632805,23080158080150,113414575414245,557601196738190
%N a(n) = number of integer strings s(0),...,s(n) counted by array T in A026374 that have s(n)=3; also a(n) = T(2n-1,n-2).
%H Vincenzo Librandi, <a href="/A026379/b026379.txt">Table of n, a(n) for n = 2..300</a>
%F a(n) = [t^(n+1)]{(1+t)(1+3t+t^2)^(n-1)}. - _Emeric Deutsch_, Jan 30 2004
%F G.f.: -1/x+2-2*x^2/(10*x^2+sqrt(1-5*x)*sqrt(1-x)*(4*x-1)-7*x+1). - _Vladimir Kruchinin_, Aug 11 2015
%p sum(binomial(n,k)*binomial(2*k+1,k-1),k=0..n); n=0,1,... # _N. J. A. Sloane_
%t a[n_] := (n-1)*Hypergeometric2F1[5/2, 2-n, 4, -4]; Table[a[n], {n, 2, 23}](* _Jean-François Alcover_, Jun 12 2012, after _N. J. A. Sloane_ *)
%t Table[Sum[Binomial[n,k]Binomial[2k+1,k-1],{k,0,n}],{n,30}] (* _Harvey P. Dale_, Apr 28 2013 *)
%Y Partial sums of A034942.
%K nonn,nice,easy
%O 2,2
%A _Clark Kimberling_
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