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%I M4945 N2118 #57 Sep 08 2022 08:44:30
%S 1,14,147,1408,13013,118482,1071799,9668036,87099705,784246870,
%T 7059619931,63542171784,571901915677,5147206719578,46325218390143,
%U 416928397167052,3752361301126529,33771274616631006,303941563175648035,2735474435084708240,24619271381777877861
%N Expansion of 1/((1-x)*(1-4*x)*(1-9*x)).
%D 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.
%D J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D T. N. Thiele, Interpolationsrechnung. Teubner, Leipzig, 1909, p. 35.
%H G. C. Greubel, <a href="/A002451/b002451.txt">Table of n, a(n) for n = 0..1000</a>
%H D. Dumont, <a href="/A001469/a001469_3.pdf">Interprétations combinatoires des nombres de Genocchi</a>, Duke Math. J., 41 (1974), 305-318. (Annotated scanned copy)
%H Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14,-49,36).
%F a(n) = 1/24 - 4^(n+2)/15 + 9^(n+2)/40. - _Antonio Alberto Olivares_, Feb 03 2010
%F a(n) = 13*a(n-1) - 36*a(n-2) + 1, n >= 2. - _Vincenzo Librandi_, Mar 23 2011
%p a:=n->sum((9^(n-j)-4^(n-j))/5,j=0..n): seq(a(n), n=1..30); # _Zerinvary Lajos_, Jan 15 2007
%p A002451:=-1/(z-1)/(4*z-1)/(9*z-1); # _Simon Plouffe_ in his 1992 dissertation
%t CoefficientList[Series[1/((1-x)(1-4x)(1-9x)), {x, 0, 30}], x] (* _Vladimir Joseph Stephan Orlovsky_, Jun 20 2011 *)
%o (PARI) Vec(1/((1-x)*(1-4*x)*(1-9*x))+O(x^30)) \\ _Charles R Greathouse IV_, Sep 23 2012
%o (GAP) List([0..30],n->1/24-4^(n+2)/15+9^(n+2)/40); # _Muniru A Asiru_, Dec 18 2018
%o (Magma) [(10 - 4^(n+4) +6*9^(n+2))/240: n in [0..30]]; // _G. C. Greubel_, Jul 04 2019
%o (Sage) [(10 - 4^(n+4) +6*9^(n+2))/240 for n in (0..30)] # _G. C. Greubel_, Jul 04 2019
%Y A diagonal of A036969.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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