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Search: id:A120306
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| A120306 |
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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]. |
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+0
1
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| 1, 9, 68, 1364, 12064, 58303, 4517375, 1142991, 4251679307, 138473652271, 240881487689, 857560784067, 49571162119157, 12805922830496929, 167798784068528807, 365691567246838709, 46160923354240494523
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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FORMULA
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a(n) = Numerator[Sum[Sum[(2i)!/(i!)^2/(i+1)/((2j)!/(j!)^2/(j+1)),{i,1,n}],{j,1,n}]].
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MATHEMATICA
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Numerator[Table[Sum[Sum[(2i)!/(i!)^2/(i+1)/((2j)!/(j!)^2/(j+1)), {i, 1, n}], {j, 1, n}], {n, 1, 20}]]
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CROSSREFS
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Cf. A000108, A014138, A007645.
Sequence in context: A121633 A091708 A024119 this_sequence A089379 A072258 A125372
Adjacent sequences: A120303 A120304 A120305 this_sequence A120307 A120308 A120309
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KEYWORD
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frac,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 14 2006
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