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A109034
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First differences of A109033.
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1
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1, 0, 1, 4, 16, 66, 280, 1216, 5384, 24224, 110464, 509480, 2372704, 11142656, 52709600, 250933120, 1201354240, 5780413760, 27937867520, 135574988800, 660314620160, 3226731934720, 15815752724480, 77735943378560
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| Ian Le, Wilf classes of pairs of permutations of length 4, The Electronic J. of Combinatorics, 12, 2005, R25.
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FORMULA
| G.f. A(x) = y satisfies 0 = 2*x*y^2 - y + (1-x)^2. - Michael Somos, Jan 05 2012
Given g.f. A(x), then B(x) = (A(x) - 1) / x satisfies B(-B(-x)) = x and B(x) - x = 4 * (B(x) * x) + 2 * (B(x) * x)^2. - Michael Somos, Jan 05 2012
G.f.: 2 * (1 - x)^2 / (1 + sqrt(1 - 8*x + 16*x^2 - 8*x^3)). - Michael Somos, Jan 05 2012
G.f.=[1-sqrt(1-8x+16x^2-8x^3)]/[4x]
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EXAMPLE
| 1 + x^2 + 4*x^3 + 16*x^4 + 66*x^5 + 280*x^6 + 1216*x^7 + 5384*x^8 + ...
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MAPLE
| G:=(1-sqrt(1-8*x+16*x^2-8*x^3))/4/x: Gser:=series(G, x=0, 30): 1, seq(coeff(Gser, x^n), n=1..27);
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MATHEMATICA
| Join[{1}, Differences[CoefficientList[Series[(1-Sqrt[1-8x+16x^2-8x^3])/ (4x(1-x)), {x, 0, 30}], x]]] (* From Harvey P. Dale, July 06 2011 *)
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PROG
| (PARI) {a(n) = if( n<0, 0, polcoeff( 2 * (1 - x)^2 / (1 + sqrt(1 - 8*x + 16*x^2 - 8*x^3 + x * O(x^n))), n))} /* Michael Somos, Jan 05 2012 */
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CROSSREFS
| Cf. A109033.
Sequence in context: A026762 A082307 A099782 * A110276 A026883 A151242
Adjacent sequences: A109031 A109032 A109033 * A109035 A109036 A109037
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 16 2005
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