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A120279
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Sum[Sum[(i+j)!/i!/j!,{i,1,j}],{j,1,n}].
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0
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2, 11, 45, 170, 631, 2346, 8780, 33089, 125466, 478181, 1830258, 7030557, 27088856, 104647615, 405187809, 1571990918, 6109558567, 23782190466, 92705454875, 361834392094, 1413883873953, 5530599237752, 21654401079301, 84859704298176
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| p divides a(p-1) and a(p-2) for prime p=5,11,17,23,29,41,47,53,59,71..=A007528[n] Primes of form 6n-1. p divides a([(2p-1)/2]) for prime p=5,11,17,23,29,41,47,53,59,71..=A007528[n] Primes of form 6n-1. p divides a((p-5)/2) for prime p=17,29,41,53,89,101.. =A040115[n] Primes of form 12n+5. Primes congruent to 5 (mod 12) excluding 5. p divides a((p-5)/3) for prime p=11,17,23,29,41,47,53,59,71..=A007528[n] Primes of form 6n-1 excluding 5 p divides a([(p-3)/3]) for prime p=11,17,23,29,41,47,53,59,71..=A007528[n] Primes of form 6n-1 excluding 5.
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FORMULA
| a(n) = Sum[Sum[(i+j)!/i!/j!,{i,1,j}],{j,1,n}]. a(n) = A079309(n+1) - (n+1). a(n) = A066796(n+1)/2 - (n+1).
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MATHEMATICA
| Table[Sum[Sum[(i+j)!/i!/j!, {i, 1, j}], {j, 1, n}], {n, 1, 50}]
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CROSSREFS
| Cf. A007528, A007528, A040115, A048775, A079309, A079309, A066796.
Sequence in context: A110679 A127109 A054208 * A037751 A037639 A000176
Adjacent sequences: A120276 A120277 A120278 * A120280 A120281 A120282
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 05 2006
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