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A002451
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Expansion of 1/((1-x)(1-4x)(1-9x)).
(Formerly M4945 N2118)
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4
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1, 14, 147, 1408, 13013, 118482, 1071799, 9668036, 87099705, 784246870, 7059619931, 63542171784, 571901915677, 5147206719578, 46325218390143, 416928397167052, 3752361301126529, 33771274616631006, 303941563175648035, 2735474435084708240, 24619271381777877861
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.
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LINKS
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index to sequences with linear recurrences with constant coefficients, signature (14,-49,36).
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FORMULA
| a(n) = 1/24 - 4^(n+2)/15 + 9^(n+2)/40. [From Antonio A. Olivares (olivares14031(AT)yahoo.com), Feb 03 2010]
a(n) = 13*a(n-1) -36*a(n-2)+1, n>=2. - Vincenzo Librandi, Mar 23 2011
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MAPLE
| a:=n->sum((9^(n-j)-4^(n-j))/5, j=0..n): seq(a(n), n=1..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 15 2007
A002451:=-1/(z-1)/(4*z-1)/(9*z-1); [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| CoefficientList[Series[1/((1 - x) (1 - 4 x) (1 - 9 x)), {x, 0, 25}], x] (* From Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)
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CROSSREFS
| A diagonal of A036969.
Sequence in context: A016278 A132934 A027473 * A016170 A081201 A065899
Adjacent sequences: A002448 A002449 A002450 * A002452 A002453 A002454
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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