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Search: id:A121323
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| A121323 |
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An A053984-like Bessel-Binet recursion found by Bob Hanlon's new survey program: a[n] = (2*n + 1)*a[n - 1] - a[n - 2]. |
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1
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| 0, 1, 5, 34, 301, 3277, 42300, 631223, 10688491, 202450106, 4240763735, 97335115799, 2429137131240, 65489367427681, 1896762518271509, 58734148698989098, 1936330144548368725, 67712820910493916277
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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I had theorized that there were a related kind of Bessel-Binets of the form: a[n]=(a0*n+c0)*a[n-1]+b0*a[n-2] Where the a0,b0 and c0 were Integers. Bob Hanlon found ones with a0=2 in a program he wrote. A053984 was already in OEIS.
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FORMULA
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a(n) = (2*n + 1)*a(n - 1) - a(n - 2) a(n)=(1/2) pi BesselJ[3/2 + n, 1] BesselY[3/2, 1] - (1/2) pi BesselJ[3/2, 1] BesselY[3/2 + n, 1]
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MATHEMATICA
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f[n_Integer] = Module[{a}, a[n] /. RSolve[{a[n] == (2*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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CROSSREFS
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Cf. A053984, A001503.
Sequence in context: A116435 A090367 A111557 this_sequence A068475 A097817 A133297
Adjacent sequences: A121320 A121321 A121322 this_sequence A121324 A121325 A121326
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula and Bob Hanlon (rlbagulatftn(AT)yahoo.com), Sep 05 2006
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