0,2

p divides a(p-1) and a((p-3)/2) for prime p=7,13,19,31,37,43,61,67..=A002476[n] Primes of form 6n + 1. p divides a((p-5)/2) for prime p=13,37,61,73,97,109..=A068228[n] Primes congruent to 1 (mod 12). p divides a(2p+1) for prime p=2,3,5,7,11,17,23,29,41,47,53,59,71.. All primes except 13,19,31,37,43,61,67..=A002476[n] Primes of form 6n + 1 excluding 7. p divides a(3p+1) for prime p=3,5,7,11,17,23,29,41,47.. All odd primes except 13,19,31,37,43..=A002476[n] Primes of form 6n + 1 excluding 7. p^2 divides a(p^2-1) for prime p>3. p divides a(3p^3+1) for prime p=2,3,5,7,11.. p^2 divides a(3p^3+1) for prime p=2,3,5,11.. p^3 divides a(3p^3+1) for prime p=2,5.. 2^9 divides a(25). - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2006

Equals triangle A106270(unsigned) * [1, 2, 3,...]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 02 2009]

1*C(n) + 2*C(n-1) + 3*C(n-2) + ... + (n+1-k)*C(k) + ... + n*C(1) + (n+1)*C(0), where C(k) = (2k)!/k!/(k+1)! is Catalan Number A000108[k]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2006

a(n) = Sum[Sum[(2k)!/k!/(k+1)!,{k,0,m}],{m,0,n}]. a(n) = Sum[(n+1-k)*(2k)!/k!/(k+1)!,{k,0,n}]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2006

Table[Sum[Sum[(2k)!/k!/(k+1)!, {k, 0, m}], {m, 0, n}], {n, 0, 50}] Table[Sum[(n+1-k)*(2k)!/k!/(k+1)!, {k, 0, n}], {n, 0, 50}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2006

Cf. A000108.

Cf. A014137.

A106270 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 02 2009]

Sequence in context: A010912 A052967 A152090 this_sequence A103439 A147321 A103030

Adjacent sequences: A014137 A014138 A014139 this_sequence A014141 A014142 A014143

nonn

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 04 2006