|
Search: id:A002621
|
|
|
| A002621 |
|
Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*(1-x^4)).
(Formerly M1051 N0394)
|
|
+0
3
|
|
| 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; listen)
|
|
|
OFFSET
|
0,2
|
|
|
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).
|
|
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).
|
|
MAPLE
|
A002621 := proc(n) local s, x ; s := taylor(1/(1-x)^2, x=0, n+1) ; s := taylor(s/(1-x^2), x=0, n+1) ; s := taylor(s/(1-x^3), x=0, n+1) ; s := taylor(s/(1-x^4), x=0, n+1) ; coeftayl(s, x=0, n) ; end: for n from 0 to 80 do printf("%d, ", A002621(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 06 2007
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
|
|
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
|
|
CROSSREFS
|
Partial sums of A001400.
Sequence in context: A011909 A065962 A049703 this_sequence A033500 A003318 A035300
Adjacent sequences: A002618 A002619 A002620 this_sequence A002622 A002623 A002624
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 06 2007
|
|
|
Search completed in 0.002 seconds
|
