A372904 Numbers k that divide the k-th central trinomial coefficient.

1, 21, 387, 657, 6291, 16113, 25767, 54243, 56457, 96141, 155601, 294273, 300871, 453781, 653421, 660879, 669609, 951881, 993307, 1246077, 1438623, 1535409, 1870533, 2110941, 2510109, 2959173, 2974239, 3158541, 3242673, 3569337, 4139739, 4789273, 5405643, 7034097

Offset

1,2

Comments

Numbers k such that k | A002426(k).

Also, numbers k that divide the k-th Riordan number: k | A005043(k).

Apparently a subsequence of A266969.

Links

Amiram Eldar, Table of n, a(n) for n = 1..38

Example

21 is a term since A002426(21) = 1105350729 = 21 * 52635749 is divisible by 21.

Mathematica

Select[Range[1000], Divisible[4^#*JacobiP[#, -# - 1/2, -# - 1/2, -1/2], #] &]

Prog

(PARI) lista(kmax) = {my(ct0 = 1, ct1 = 1, ct2); print1("1, "); for(k = 2, kmax, ct2 = ((2*k-1)*ct1 + 3*(k-1)*ct0)/k; if(!(ct2 % k), print1(k, ", ")); ct0 = ct1; ct1 = ct2); }

Crossrefs

Cf. A002426, A005043.

Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).

Sequence in context: A108740 A297455 A256178 * A094172 A296723 A145613

Adjacent sequences: A372901 A372902 A372903 * A372905 A372906 A372907

Keyword

nonn

Author

Amiram Eldar, May 16 2024

Status

approved