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A002453
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Central factorial numbers.
(Formerly M5249 N2283)
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4
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1, 35, 966, 24970, 631631, 15857205, 397027996, 9931080740, 248325446061, 6208571999575, 155218222621826, 3880490869237710, 97012589464171291, 2425317596203339145, 60632965641474990456, 1515824372664398367880
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OFFSET
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0,2
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REFERENCES
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A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 112.
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
T. N. Thiele, Interpolationsrechnung. Teubner, Leipzig, 1909, p. 36.
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LINKS
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FORMULA
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G.f.: 1/((1 - x)*(1 - 9*x)*(1 - 25*x)).
a(n) = (5^(2*n + 4) - 3^(2*n + 5) + 2)/384.
E.g.f.: sinh(x)^5/120 = Sum_{n>=0} a(n)*x^(2*n + 5)/(2*n + 5)!. - Vladimir Kruchinin, Sep 30 2012
a(n) = det(|v(i+3,j+2)|, 1 <= i,j <= n), where v(n,k) are central factorial numbers of the first kind with odd indices (A008956). - Mircea Merca, Apr 06 2013
a(n) = 35*a(n-1) -259*a(n-2) +225*a(n-3), with a(0) = 1, a(1) = 35, a(2) = 966. - Harvey P. Dale, Feb 25 2015
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MAPLE
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MATHEMATICA
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CoefficientList[Series[1/((1-x)(1-9x)(1-25x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{35, -259, 225}, {1, 35, 966}, 20] (* Harvey P. Dale, Feb 25 2015 *)
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PROG
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(GAP) List([0..20], n->(5^(2*n+4)-3^(2*n+5)+2)/384); # Muniru A Asiru, Dec 20 2018
(PARI) vector(20, n, n--; (5^(2*n+4)-3^(2*n+5)+2)/384) \\ G. C. Greubel, Jul 04 2019
(Magma) [(5^(2*n+4)-3^(2*n+5)+2)/384: n in [0..20]]; // G. C. Greubel, Jul 04 2019
(Sage) [(5^(2*n+4)-3^(2*n+5)+2)/384 for n in (0..20)] # G. C. Greubel, Jul 04 2019
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CROSSREFS
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Right-hand column 2 in triangle A008958.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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