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 A338036 Triangle T(n,m) = Sum_{k=1..m} C(2*m-k-1,m-k)*C(2*(2*m-k),n-2*m+k), n>0, m>0. 1

%I

%S 1,2,1,1,6,1,0,18,9,1,0,34,45,12,1,0,41,164,78,15,1,0,30,453,376,120,

%T 18,1,0,12,936,1490,695,171,21,1,0,2,1429,4916,3305,1158,231,24,1,0,0,

%U 1596,13266,13647,6333,1792,300,27,1

%N Triangle T(n,m) = Sum_{k=1..m} C(2*m-k-1,m-k)*C(2*(2*m-k),n-2*m+k), n>0, m>0.

%F G.f.: 2*x^2*(x+1)^4/(1-4*x^2*(x+1)^4*y+(2*x*(x+1)^2-1)*sqrt(1-4*x^2*(x+1)^4*y)).

%e 1,

%e 2,1,

%e 1,6,1,

%e 0,18,9,1,

%e 0,34,45,12,1,

%e 0,41,164,78,15,1,

%e 0,30,453,376,120,18,1

%t T[n_, m_] := Sum[Binomial[2*m - k - 1, m - k] * Binomial[2*(2*m - k), n - 2*m + k], {k, 1, m}]; Table[T[n, m], {n, 1, 10}, {m, 1, n}] // Flatten (* _Amiram Eldar_, Oct 08 2020 *)

%o (Maxima)

%o T(n,m):=sum(binomial(2*m-k-1,m-k)*binomial(2*(2*m-k),n-2*m+k),k,1,m);

%K nonn,tabl

%O 1,2

%A _Vladimir Kruchinin_, Oct 07 2020

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Last modified August 6 00:36 EDT 2021. Contains 346493 sequences. (Running on oeis4.)