OFFSET
0,2
REFERENCES
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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..710
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (35,-259,225).
FORMULA
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
a(n) = 25*a(n-1) + A002452(n+1), with a(0) = 1. - Nadia Lafreniere, Aug 08 2022
MAPLE
A002453:=-1/(z-1)/(25*z-1)/(9*z-1); # Simon Plouffe (from his 1992 dissertation).
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved