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A338035 Triangle T(n,m) = (1/m)*Sum_{k=1..m} k*C(2*m-k-1,m-k)*C(2*(2*m-k),n-2*m+k), n>0, m>0. 0

%I #13 Oct 14 2020 11:10:13

%S 1,2,1,1,5,1,0,12,8,1,0,19,33,11,1,0,21,96,63,14,1,0,15,217,256,102,

%T 17,1,0,6,386,830,524,150,20,1,0,1,533,2241,2147,927,207,23,1,0,0,560,

%U 5079,7440,4541,1492,273,26,1

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

%F G.f.: 1/(1-(1-sqrt(x*(-4*x^5-16*x^4-24*x^3-16*x^2-4*x)*y+1))/(2*x^3+4*x^2+2*x)).

%e 1,

%e 2,1,

%e 1,5,1,

%e 0,12,8,1,

%e 0,19,33,11,1,

%e 0,21,96,63,14,1,

%e 0,15,217,256,102,17,1

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

%o (Maxima)

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

%Y Cf. A338036, A338037.

%K nonn,tabl

%O 1,2

%A _Vladimir Kruchinin_, Oct 07 2020

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)