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%I #31 Nov 09 2021 18:11:07
%S 1,4,3,11,15,5,29,56,35,7,76,189,171,66,9,199,605,715,407,110,11,521,
%T 1872,2730,2054,832,169,13,1364,5655,9810,9180,4965,1533,245,15,3571,
%U 16779,33745,37774,25585,10642,2618,340,17,9349,49096,112309,146357,119168,62453,20862,4218,456,19
%N Coefficients of a generalized Jaco-Lucas polynomial (odd indices) read by rows.
%C Alternating row sums seem to be 1. - _F. Chapoton_, Nov 09 2021
%H Y. Sun, <a href="https://www.fq.math.ca/Papers1/43-4/paper43-4-10b.pdf">Numerical Triangles and Several Classical Sequences</a>, Fib. Quart. 43, no. 4, (2005) 359-370, Table 3.4.
%F T(n,k) = Sum_{j=0..n} (2n+1)*binomial(2n+1-j,j)*binomial(j,k)/(2n+1-j).
%e Triangle begins:
%e 1,
%e 4, 3,
%e 11, 15, 5,
%e 29, 56, 35, 7,
%e 76, 189, 171, 66, 9,
%e ...
%p A200073 := proc(n,k)
%p (2*n+1)*add( binomial(2*n+1-j,j)*binomial(j,k)/(2*n+1-j),j=0..n) ;
%p end proc:
%p seq(seq(A200073(n,k),k=0..n),n=0..13) ; # _R. J. Mathar_, Nov 13 2011
%t T[n_, k_] := Sum[(2n+1) Binomial[2n+1-j, j] Binomial[j, k]/(2n+1-j), {j, 0, n}];
%t Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Apr 02 2020 *)
%Y Cf. A002878 (first column), A005408 (diagonal).
%K nonn,tabl
%O 0,2
%A _N. J. A. Sloane_, Nov 13 2011
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