A002451 Expansion of 1/((1-x)*(1-4*x)*(1-9*x)). (Formerly M4945 N2118)

1, 14, 147, 1408, 13013, 118482, 1071799, 9668036, 87099705, 784246870, 7059619931, 63542171784, 571901915677, 5147206719578, 46325218390143, 416928397167052, 3752361301126529, 33771274616631006, 303941563175648035, 2735474435084708240, 24619271381777877861

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. 35.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

D. Dumont, Interprétations combinatoires des nombres de Genocchi, Duke Math. J., 41 (1974), 305-318. (Annotated scanned copy)

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 (14,-49,36).

Formula

a(n) = 1/24 - 4^(n+2)/15 + 9^(n+2)/40. - Antonio Alberto Olivares, Feb 03 2010

a(n) = 13*a(n-1) - 36*a(n-2) + 1, n >= 2. - Vincenzo Librandi, Mar 23 2011

Maple

a:=n->sum((9^(n-j)-4^(n-j))/5, j=0..n): seq(a(n), n=1..30); # Zerinvary Lajos, Jan 15 2007
A002451:=-1/(z-1)/(4*z-1)/(9*z-1); # Simon Plouffe in his 1992 dissertation

Mathematica

CoefficientList[Series[1/((1-x)(1-4x)(1-9x)), {x, 0, 30}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)

Prog

(PARI) Vec(1/((1-x)*(1-4*x)*(1-9*x))+O(x^30)) \\ Charles R Greathouse IV, Sep 23 2012
(GAP) List([0..30], n->1/24-4^(n+2)/15+9^(n+2)/40); # Muniru A Asiru, Dec 18 2018
(Magma) [(10 - 4^(n+4) +6*9^(n+2))/240: n in [0..30]]; // G. C. Greubel, Jul 04 2019
(Sage) [(10 - 4^(n+4) +6*9^(n+2))/240 for n in (0..30)] # G. C. Greubel, Jul 04 2019

Crossrefs

A diagonal of A036969.

Sequence in context: A209347 A132934 A027473 * A302994 A207259 A016170

Adjacent sequences: A002448 A002449 A002450 * A002452 A002453 A002454

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved