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A002621 Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*(1-x^4)).
(Formerly M1051 N0394)
13
1, 2, 4, 7, 12, 18, 27, 38, 53, 71, 94, 121, 155, 194, 241, 295, 359, 431, 515, 609, 717, 837, 973, 1123, 1292, 1477, 1683, 1908, 2157, 2427, 2724, 3045, 3396, 3774, 4185, 4626, 5104, 5615, 6166, 6754, 7386, 8058, 8778, 9542, 10358, 11222, 12142, 13114 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

E. Fix and J. L. Hodges, Jr., Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312.

E. Fix and J. L. Hodges, Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312. [Annotated scanned copy]

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 199

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.

Thomas Wieder, The number of certain k-combinations of an n-set, Applied Mathematics Electronic Notes, vol. 8 (2008).

Index entries for linear recurrences with constant coefficients, signature (2, 0, -1, 0, -2, 2, 0, 1, 0, -2, 1).

FORMULA

a(n) = +2*a(n-1) - a(n-3) - 2*a(n-5) + 2*a(n-6) + a(n-8) - 2*a(n-10) + a(n-11).

a(n) = 83*n^2/288 +55*n/64 +2815/3456 +11*n^3/288 +n^4/576 +11*(-1)^n/128 +(-1)^n*n/64 + A057077(n)/16 +A061347(n)/27. - R. J. Mathar, Mar 15 2011

a(n)=floor((n+1)*(9*(-1)^n + n^3 + 21*n^2 + 145*n + 350)/576 + 1/2). - Tani Akinari, Nov 10 2012

MAPLE

A002621:=-1/(z**2+1)/(z**2+z+1)/(z+1)**2/(z-1)**5; # Simon Plouffe in his 1992 dissertation

with(combstruct):ZL:=[st, {st=Prod(left, right), left=Set(U, card=r+2), right=Set(U, card<r), U=Sequence(Z, card>=1)}, unlabeled]: subs(r=2, stack): seq(count(subs(r=2, ZL), size=m), m=4..51) ; # Zerinvary Lajos, Feb 07 2008

A057077 := proc(n) (-1)^floor(n/2) ; end proc:

A061347 := proc(n) op(1+(n mod 3), [1, 1, -2]) ; end proc:

A002621 := proc(n) 83/288*n^2+55/64*n+2815/3456+11/288*n^3+1/576*n^4+11/128*(-1)^n+1/64*(-1)^n*n; %+ A057077(n)/16 +A061347(n)/27; end proc:

seq(A002621(n), n=0..10) ; # R. J. Mathar, Mar 15 2011

MATHEMATICA

CoefficientList[Series[1/((1-x)^2*(1-x^2)*(1-x^3)*(1-x^4)), {x, 0, 60}], x] (* Stefan Steinerberger, Jun 10 2007 *)

LinearRecurrence[{2, 0, -1, 0, -2, 2, 0, 1, 0, -2, 1}, {1, 2, 4, 7, 12, 18, 27, 38, 53, 71, 94}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 23 2012 *)

PROG

(PARI) a(n)=(n+1)*(9*(-1)^n+n^3+21*n^2+145*n+350)\/576 \\ Charles R Greathouse IV, May 23 2013

CROSSREFS

Partial sums of A001400. Column 4 of A092905.

Sequence in context: A173722 A049703 A175812 * A033500 A003318 A035300

Adjacent sequences:  A002618 A002619 A002620 * A002622 A002623 A002624

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 15 11:03 EDT 2018. Contains 316224 sequences. (Running on oeis4.)