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A000338 Expansion of (5-2x)(1-x^3)/(1-x)^4.
(Formerly M3877 N1589)
3
5, 18, 42, 75, 117, 168, 228, 297, 375, 462, 558, 663, 777, 900, 1032, 1173, 1323, 1482, 1650, 1827, 2013, 2208, 2412, 2625, 2847, 3078, 3318, 3567, 3825, 4092, 4368, 4653, 4947, 5250, 5562, 5883, 6213, 6552, 6900, 7257, 7623, 7998, 8382, 8775, 9177, 9588, 10008, 10437, 10875, 11322, 11778 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

REFERENCES

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23.

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).

LINKS

T. D. Noe, Table of n, a(n) for n = 3..1000

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

J. Riordan, Discordant permutations, Scripta Math., 20 (1954), 14-23. [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = (9/2)*n^2 - (15/2)*n, n>2. - Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

MAPLE

ff := n->9/2*n^2-15/2*n; seq(ff(n), n=3..60); # Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

A000338:=(2*z-5)*(z**2+z+1)/(z-1)**3; # conjectured by Simon Plouffe in his 1992 dissertation

MATHEMATICA

nn = 100; CoefficientList[Series[(5 - 2 x) (1 - x^3)/(1 - x)^4, {x, 0, nn}], x] (* T. D. Noe, Jun 19 2012 *)

LinearRecurrence[{3, -3, 1}, {5, 18, 42, 75}, 60] (* Harvey P. Dale, Sep 20 2016 *)

CROSSREFS

Sequence in context: A225272 A276819 A236364 * A212343 A056640 A272703

Adjacent sequences:  A000335 A000336 A000337 * A000339 A000340 A000341

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Barbara Haas Margolius (margolius(AT)math.csuohio.edu), Feb 17 2001

STATUS

approved

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Last modified May 24 17:40 EDT 2017. Contains 286997 sequences.