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

0,2

Comments

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

Links

Table of n, a(n) for n=0..54.

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

Formula

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A086564 A316966 A295727 * A080777 A001166 A065337

Adjacent sequences: A200070 A200071 A200072 * A200074 A200075 A200076

Keyword

nonn,tabl

Author

N. J. A. Sloane, Nov 13 2011

Status

approved