A087178 ((1/2)/p^2)*(T(p)-1) where p runs through the prime >= 5 and T(k) is the k-th central trinomial number (A002426).

1, 4, 106, 630, 26185, 178666, 8991709, 3678166249, 28031525940, 13143231877116, 824038411943548, 6585233816779471, 427212999940414402, 230740449590738871715, 128696758387000610268418, 1065763722815793191814814, 614675485079469646826034034

Offset: 1

Author

Benoit Cloitre, Oct 19 2003

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..317

Crossrefs

Cf. A002426.

Programs

Mathematica

f[0] = f[1] = 1; f[n_] := f[n] = ((2*n-1)*f[n-1] + 3*(n-1)*f[n-2])/n; Table[(f[p]-1)/(2*p^2), {p, Prime[Range[3, 20]]}] (* Amiram Eldar, Apr 21 2025 *)

Formula

T(n) == 1 (mod n^2) iff n is prime.