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 A217525 From the enumeration of involutions avoiding the pattern 4321. 1
 0, 0, 0, 0, 0, 2, 4, 6, 15, 31, 67, 155, 343, 787, 1829, 4233, 9940, 23454, 55540, 132390, 316704, 760462, 1833050, 4431552, 10745282, 26125316, 63672044, 155536070, 380739734, 933832952, 2294581836, 5647750518, 13923153431, 34375447863, 84989987987, 210407135915, 521547749731, 1294310608775, 3215632551785, 7997467696213, 19910095233857 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Piera Manara and Claudio Perelli Cippo, The fine structure of 4321 avoiding involutions and 321 avoiding involutions, PU. M. A. Vol. 22 (2011), 227-238; See Theorem 4.2. FORMULA Manara and Cippo give a g.f. MAPLE A217525 := proc(nmax)     local x ;     -4+4/(1+x^2)+1/(1+x)^2 ;     1/(1+x)-2*x^2*(1+x)-sqrt(%) ;     taylor(%/2, x=0, nmax+1) ;     seq(coeftayl(%, x=0, n), n=0..nmax) ; end proc: # R. J. Mathar, Nov 05 2012 MATHEMATICA a[n_] := SeriesCoefficient[(1/2)(-2(x+1)x^2 - Sqrt[4/(x^2+1) + 1/(x+1)^2 - 4] + 1/(x+1)), {x, 0, n}]; a /@ Range[0, 40] (* Jean-François Alcover, Apr 04 2020 *) CROSSREFS Sequence in context: A275664 A192536 A227902 * A295615 A127679 A049022 Adjacent sequences:  A217522 A217523 A217524 * A217526 A217527 A217528 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 13 2012 STATUS approved

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Last modified May 18 04:22 EDT 2021. Contains 343994 sequences. (Running on oeis4.)