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Search: id:A121627
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| A121627 |
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Real part of a complex operation analogous to the factorials. |
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+0
1
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| 1, 0, -12, -96, -480, 0, 40320, 645120, 5806080, 0, -1277337600, -30656102400, -398529331200, 0, 167382319104000, 5356234211328000, 91055981592576000, 0, -62282291409321984000, -2491291656372879360000, -52317124783830466560000, 0
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Conjecture (1): Current nonzero term divides next nonzero term; as an operation, getting a new sequence: 12, 8, 5, 84, 16, 9, 220, 24, 13...; using unsigned terms). Example: a(5) = -480, and a(7)= 40320, the next nonzero term in the sequence. Then 40320/480 = 84. Conjecture (2): If the term in (12, 8, 5...) is generated from a(n)/a(n-1) or a(n)/a(n-2), then n divides each (12, 8, 5...). Example: a(11) = -1277337600 and the previous nonzero term = a(9) = 5806080. Then a(11)/a(9) = 220, and 11 divides 220: 220/11 = 20.
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FORMULA
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Let a(1) = 1, real part of (1 + i) = k(1); then k(n) = (n + ni) * k(n-1), n>1. a(n) = real part of each k(n).
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EXAMPLE
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a(3) = -12 since a(1) = (1 + i); (2 + 2i)* (1 + i) = (0 +
4i); (3 + 3i)*(0 + 4i) = (-12 + 12i).
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MATHEMATICA
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a[1] = 1 + I; a[n_] := a[n] = a[n - 1]*(n + n*I); Table[Re[a[n]], {n, 22}] (* Or *)
f[n_] := Fold[(#2 + #2*I)*#1 &, 1 + I, Range@n + 1]; Table[ Re[f[n]], {n, 0, 22}] (* Robert G. Wilson v *)
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CROSSREFS
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Sequence in context: A027250 A059154 A120658 this_sequence A138162 A073392 A038845
Adjacent sequences: A121624 A121625 A121626 this_sequence A121628 A121629 A121630
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KEYWORD
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sign
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 12 2006
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EXTENSIONS
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More terms from Robert G. Wilson v, Aug 17 2006
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