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%I #8 May 17 2024 01:45:49
%S 1,21,387,657,6291,16113,25767,54243,56457,96141,155601,294273,300871,
%T 453781,653421,660879,669609,951881,993307,1246077,1438623,1535409,
%U 1870533,2110941,2510109,2959173,2974239,3158541,3242673,3569337,4139739,4789273,5405643,7034097
%N Numbers k that divide the k-th central trinomial coefficient.
%C Numbers k such that k | A002426(k).
%C Also, numbers k that divide the k-th Riordan number: k | A005043(k).
%C Apparently a subsequence of A266969.
%H Amiram Eldar, <a href="/A372904/b372904.txt">Table of n, a(n) for n = 1..38</a>
%e 21 is a term since A002426(21) = 1105350729 = 21 * 52635749 is divisible by 21.
%t Select[Range[1000], Divisible[4^#*JacobiP[#, -# - 1/2, -# - 1/2, -1/2], #] &]
%o (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);}
%Y Cf. A002426, A005043.
%Y Similar sequences: A014847 (Catalan), A016089 (Lucas), A023172 (Fibonacci), A051177 (partition), A232570 (tribonacci), A246692 (Pell), A266969 (Motzkin).
%K nonn
%O 1,2
%A _Amiram Eldar_, May 16 2024