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A112521 Sequence related to NOR bracketings.

%I A112521 #21 Jan 12 2022 01:02:54
%S A112521 0,1,0,6,4,60,84,700,1440,8910,23100,120120,360360,1684956,5552064,
%T A112521 24302520,85101456,357502860,1302562404,5333981796,19947127200,
%U A112521 80408748420,305922388200,1221485157360,4701015343440,18664243014300
%N A112521 Sequence related to NOR bracketings.
%C A112521 Conjecture: Starting with n=1, a(n) is the main diagonal of the array defined as T(1,1) = 1, T(i,j) = 0 if i<1 or j<1, T(n,k) = T(n,k-2) + T(n,k-1) -2*T(n-1,k-1) + T(n-1,k) + T(n-2,k). - _Gerald McGarvey_, Oct 07 2008
%H A112521 G. C. Greubel, <a href="/A112521/b112521.txt">Table of n, a(n) for n = 0..1000</a>
%F A112521 a(n) = Sum_{j=0..n} (-1)^(j-1)*C(2*n-j-1, n-j)*C(2*(j-1), j-1). - corrected by _Peter Bala_, Aug 19 2014
%F A112521 a(n) = n*A055392(n), n>1.
%F A112521 a(n) = binomial(2*n-2, n-1)*Hypergeometric([-(n-1), 1/2], [2-2*n], -4) with a(0) = 0, a(1) = 1. - _G. C. Greubel_, Jan 11 2022
%t A112521 a[n_]:= Sum[(-1)^j*Binomial[2*j, j]*Binomial[2*n-j-2, n-j-1], {j,0,n-1}];
%t A112521 Table[a[n], {n,0,30}] (* _G. C. Greubel_, Jan 11 2022 *)
%o A112521 (PARI) a(n) = sum(j=0,n, (-1)^(j-1)*binomial(2*n-j-1, n-j)*binomial(2*(j-1), j-1)); \\ _Michel Marcus_, Aug 19 2014
%o A112521 (Sage)
%o A112521 def a(n): return n if (n<2) else binomial(2*n-2, n-1)*simplify( hypergeometric([-(n-1), 1/2], [2-2*n], -4) )
%o A112521 [a(n) for n in (0..30)] # _G. C. Greubel_, Jan 11 2022
%Y A112521 Cf. A055392.
%K A112521 easy,nonn
%O A112521 0,4
%A A112521 _Paul Barry_, Sep 09 2005