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A007043
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Number of noncommutative SL(2,C)-invariants of degree n in 5 variables.
(Formerly M3870)
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0
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1, 0, 1, 1, 5, 16, 65, 260, 1085, 4600, 19845, 86725, 383251, 1709566, 7687615, 34812519, 158614405, 726612216, 3344696501, 15462729645, 71763732545
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| Almkvist, Gert; Dicks, Warren; Formanek, Edward; Hilbert series of fixed free algebras and noncommutative classical invariant theory. J. Algebra 93 (1985), no. 1, 189-214.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| a(n)=sum{k=0..n, sum{j=0..k, C(n,k)C(k,j)(-3)^(k-j)A000108(j)}}; a(n)=(1/(2*pi))*int((1-3x+x^2)^n*sqrt(x(4-x))/x,x,0,4); - Paul Barry (pbarry(AT)wit.ie), Oct 18 2007.
G.f.: F(G^(-1)(x)) where F(t) := (t^2+3*t+1)/((t+1)*(4*t+1)^(1/2)) and G(t) := t/(t^2+3*t+1). - Mark van Hoeij, Oct 30 2011
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MAPLE
| F := (t^2+3*t+1)/((t+1)*(4*t+1)^(1/2)); G := t/(t^2+3*t+1); Ginv := RootOf(numer(G-x), t); ogf := series(eval(F, t=Ginv), x=0, 20); - Mark van Hoeij, Oct 30 2011
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CROSSREFS
| Sequence in context: A034532 A092497 A026525 * A128242 A166932 A027105
Adjacent sequences: A007040 A007041 A007042 * A007044 A007045 A007046
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein (mira(AT)math.berkeley.edu)
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