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A120305
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Sum[Sum[(-1)^(i+j)*(i+j)!/(i!j!),{i,0,n}],{j,0,n}].
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0
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1, 1, 3, 9, 31, 111, 407, 1513, 5679, 21471, 81643, 311895, 1196131, 4602235, 17757183, 68680169, 266200111, 1033703055, 4020716123, 15662273839, 61092127491, 238582873475, 932758045123, 3650336341239, 14298633670931
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| p divides a((p+1)/2) for prime p=3,11,17,19,41,43,59,67,73,83,89,97,107,113..=A033200[n] Primes congruent to {1, 3} mod 8; or, odd primes of form x^2+2*y^2. p divides a((p-3)/2) for prime p=17,41,73,89,97,113,137..=A007519[n] Primes of form 8n+1.
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FORMULA
| a(n) = Sum[Sum[(-1)^(i+j)*(i+j)!/(i!j!),{i,0,n}],{j,0,n}].
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MATHEMATICA
| Table[Sum[Sum[(-1)^(i+j)*(i+j)!/(i!j!), {i, 0, n}], {j, 0, n}], {n, 0, 50}]
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CROSSREFS
| Cf. A033200, A007519.
Sequence in context: A151459 A151033 A047012 * A049170 A049174 A049159
Adjacent sequences: A120302 A120303 A120304 * A120306 A120307 A120308
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KEYWORD
| nonn
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AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 14 2006
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