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A002621
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Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*(1-x^4)).
(Formerly M1051 N0394)
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3
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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; internal format)
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OFFSET
| 0,2
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REFERENCES
| E. Fix and J. L. Hodges, Jr., Significance probabilities of the Wilcoxon test, Annals Math. Stat., 26 (1955), 301-312.
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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
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.
P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 199
Thomas Wieder, The number of certain k-combinations of an n-set, Applied Mathematics Electronic Notes, vol. 8 (2008).
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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
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MAPLE
| A002621:=-1/(z**2+1)/(z**2+z+1)/(z+1)**2/(z-1)**5; [S. 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 (zerinvarylajos(AT)yahoo.com), 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
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MATHEMATICA
| CoefficientList[Series[1/((1-x)^2*(1-x^2)*(1-x^3)*(1-x^4)), {x, 0, 60}], x] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 10 2007
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CROSSREFS
| Partial sums of A001400.
Sequence in context: A173722 A049703 A175812 * A033500 A003318 A035300
Adjacent sequences: A002618 A002619 A002620 * A002622 A002623 A002624
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 06 2007
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