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A372904
Numbers k that divide the k-th central trinomial coefficient.
1
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
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 16 2024
STATUS
approved