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A121354
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a(n) = (3*n-1)*a(n-1) - a(n-2).
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1
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0, 1, 5, 39, 424, 5897, 99825, 1990603, 45684044, 1185794541, 34342357645, 1097769650099, 38387595395820, 1457630855391061, 59724477475637681, 2626419378072666903, 123381986291939706760, 6166472895218912671097
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n)= Pi* ( J_{n+2/3}(2/3) * Y_{2/3}(2/3) - J_{2/3}(2/3)* Y_{n+2/3}(2/3) )/3 , where J and Y are Bessel functions.
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MATHEMATICA
| f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == (3*n - 1)*a[n - 1] - a[n - 2], a[0] == 0, a[1] == 1}, a[n], n][[1]] // FullSimplify] Rationalize[N[Table[f[n], {n, 0, 25}], 100], 0]
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PROG
| (python3) # replace triple dots by tabs
def A121354(n):
...if n<= 1:
......return n
...else:
......return (3*n-1)*A121354(n-1)-A121354(n-2)
print([A121354(n) for n in range(0, 20)]) # Oct 14 2009
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CROSSREFS
| Cf. A053984, A001503.
Sequence in context: A124549 A024216 A127189 * A122486 A199244 A193118
Adjacent sequences: A121351 A121352 A121353 * A121355 A121356 A121357
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KEYWORD
| nonn,easy
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AUTHOR
| Roger Bagula and Bob Hanlon (rlbagulatftn(AT)yahoo.com), Sep 05 2006
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EXTENSIONS
| Offset corrected by the Associate Editors of the OEIS - Oct 14 2009
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