|
| |
|
|
A120306
|
|
Numerator of the sum of all matrix elements of n X n matrix M[i,j]=CatalanNumber[i]/CatalanNumber[j], where CatalanNumber[k]=(2k)!/k!/(k+1)!=A000108[k].
|
|
0
| |
|
|
1, 9, 68, 1364, 12064, 58303, 4517375, 1142991, 4251679307, 138473652271, 240881487689, 857560784067, 49571162119157, 12805922830496929, 167798784068528807, 365691567246838709, 46160923354240494523
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| p divides a(p-1) for prime p=3,7,13,19,31,37,43,61,67..=A007645 Cuban primes: of form x^2+xy+y^2; or: primes of form x^2+3*y^2; or: primes == 0 or 1 mod 3.
|
|
|
FORMULA
| a(n) = Numerator[Sum[Sum[(2i)!/(i!)^2/(i+1)/((2j)!/(j!)^2/(j+1)),{i,1,n}],{j,1,n}]].
|
|
|
MATHEMATICA
| Numerator[Table[Sum[Sum[(2i)!/(i!)^2/(i+1)/((2j)!/(j!)^2/(j+1)), {i, 1, n}], {j, 1, n}], {n, 1, 20}]]
|
|
|
CROSSREFS
| Cf. A000108, A014138, A007645.
Sequence in context: A121633 A091708 A024119 * A197425 A089379 A193698
Adjacent sequences: A120303 A120304 A120305 * A120307 A120308 A120309
|
|
|
KEYWORD
| frac,nonn
|
|
|
AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 14 2006
|
| |
|
|
