A072458 Shadow transform of Catalan numbers A000108.

0, 1, 0, 0, 0, 1, 1, 2, 0, 0, 1, 4, 1, 5, 4, 1, 0, 7, 2, 8, 3, 3, 7, 10, 2, 3, 9, 0, 5, 13, 9, 14, 0, 6, 12, 4, 3, 17, 14, 8, 4, 19, 8, 20, 9, 8, 19, 22, 1, 8, 6, 10, 12, 25, 6, 11, 11, 15, 25, 28, 14, 29, 28, 10, 0, 10, 15, 32, 19, 22, 17, 34, 11, 35, 32, 15, 22, 17, 21, 38, 3, 0, 36, 40, 19, 21

Offset: 0

Author

N. J. A. Sloane, Aug 02 2002, corrected Aug 21 2002

Keywords

• nonn
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..4000
• Lorenz Halbeisen and Norbert Hungerbuehler, Number theoretic aspects of a combinatorial function, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150; see Definition 7 for the shadow transform.
• N. J. A. Sloane, Transforms.

Crossrefs

Cf. A072480.

Programs

Maple

a:= n-> add(`if`(modp(binomial(2*j,j)/(j+1), n)=0, 1, 0), j=0..n-1):
seq(a(n), n=0..120);  # Alois P. Heinz, Sep 16 2019

Mathematica

a[n_] := Sum[If[Mod[Binomial[2*j, j]/(j+1), n] == 0, 1, 0], {j, 0, n-1}];
Table[a[n], {n, 0, 120}] (* Jean-François Alcover, Jan 07 2025, after Alois P. Heinz *)