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Search: id:A131490
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| A131490 |
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Appears in Taylor series of powers of generalized Bessel functions. |
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1
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| 1, 1, 3, 16, 130, 1485, 22645, 444136, 10889676, 326345460, 11736144420, 498798542880, 24732729791484, 1415034219327729, 92523874454996985, 6856434802243346320, 571604206230905727880, 53259509403796625217288
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Integer sequence given between equations (16) and (17) of Bender et al., p. 4. A recursion is found for coefficients of Taylor series of r-th powers of generalized Bessel functions.
A001263^(-1) * [1, 2, 3,...] = A103364 * [1, 2, 3,...] = (1, 1, -1, 3, -16, 130, -1485, 22645,...); where A001263 = the Narayana triangle. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 02 2008
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LINKS
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Carl M. Bender, Dorje C. Brody, Bernhard K. Meister, On powers of Bessel functions, J. Math. Phys. vol 44, No. 1 (2003) pp 309-314.
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MAPLE
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A131490 := proc(n) local twos, resul; resul := twos*taylor(BesselI(0, twos), twos=0, 2*n+3) ; resul := resul/taylor(BesselI(1, twos), twos=0, 2*n+3) ; resul := taylor(resul-4, twos=0, 2*n+3) ; resul := coeftayl(resul, twos=0, 2*n) ; resul := resul*4^n/2 ; abs(resul*factorial(n+1)*factorial(n)) ; end: seq(A131490(n), n=1..23) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2007
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CROSSREFS
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Cf. A001263, A103364.
Sequence in context: A082161 A135752 A120021 this_sequence A121673 A051921 A023998
Adjacent sequences: A131487 A131488 A131489 this_sequence A131491 A131492 A131493
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 28 2007
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2007
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