A200073 Coefficients of a generalized Jaco-Lucas polynomial (odd indices) read by rows.

1, 4, 3, 11, 15, 5, 29, 56, 35, 7, 76, 189, 171, 66, 9, 199, 605, 715, 407, 110, 11, 521, 1872, 2730, 2054, 832, 169, 13, 1364, 5655, 9810, 9180, 4965, 1533, 245, 15, 3571, 16779, 33745, 37774, 25585, 10642, 2618, 340, 17, 9349, 49096, 112309, 146357, 119168, 62453, 20862, 4218, 456, 19

Offset: 0

Author

N. J. A. Sloane, Nov 13 2011

Keywords

• nonn
• tabl

Comments

Alternating row sums seem to be 1. - F. Chapoton, Nov 09 2021

Examples

			Triangle begins:
1,
4, 3,
11, 15, 5,
29, 56, 35, 7,
76, 189, 171, 66, 9,
...
		

Links

• Y. Sun, Numerical Triangles and Several Classical Sequences, Fib. Quart. 43, no. 4, (2005) 359-370, Table 3.4.

Crossrefs

Cf. A002878 (first column), A005408 (diagonal).

Programs

Maple

A200073 := proc(n,k)
    (2*n+1)*add( binomial(2*n+1-j,j)*binomial(j,k)/(2*n+1-j),j=0..n) ;
end proc:
seq(seq(A200073(n,k),k=0..n),n=0..13) ; # R. J. Mathar, Nov 13 2011

Mathematica

T[n_, k_] := Sum[(2n+1) Binomial[2n+1-j, j] Binomial[j, k]/(2n+1-j), {j, 0, n}];
Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* Jean-François Alcover, Apr 02 2020 *)

Formula

T(n,k) = Sum_{j=0..n} (2n+1)*binomial(2n+1-j,j)*binomial(j,k)/(2n+1-j).