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 A006251 Number of n-element posets which are unions of 2 chains. (Formerly M1216) 3
 1, 1, 2, 4, 10, 26, 75, 225, 711, 2311, 7725, 26313, 91141, 319749, 1134234, 4060128, 14648614, 53208998, 194423568, 714130372, 2635256408, 9764995800, 36320086418, 135548135854, 507434502474, 1904982684106, 7170113287574, 27051804890638, 102287657120454, 387558371409606, 1471212825012499, 5594771416613721 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 6.45. LINKS T. D. Noe, Table of n, a(n) for n=0..200 R. P. Stanley (proposer), Problem 6342, Amer. Math. Monthly, 88 (1981), 294. FORMULA G.f.: 4/(2-2*x+sqrt(1-4*x)+sqrt(1-4*x^2)). a(n) ~ (2-sqrt(3))*2^(2*n+3)/(6*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Aug 13 2013 Recurrence: (n-1)*n*(n+2)*(n^2 - 8*n + 17)*a(n) = (n-1)*(9*n^4 - 74*n^3 + 159*n^2 + 36*n - 180)*a(n-1) - 2*(n-3)*(n-2)*(n-1)*(8*n^2 - 38*n + 15)*a(n-2) - 4*(n-1)*(14*n^4 - 194*n^3 + 999*n^2 - 2244*n + 1860)*a(n-3) + 8*(22*n^5 - 354*n^4 + 2259*n^3 - 7159*n^2 + 11307*n - 7125)*a(n-4) + 16*(n^5 - 37*n^4 + 392*n^3 - 1787*n^2 + 3681*n - 2775)*a(n-5) - 32*(2*n-9)*(6*n^4 - 100*n^3 + 612*n^2 - 1638*n + 1645)*a(n-6) + 64*(n-6)*(2*n-11)*(2*n-9)*(n^2 - 6*n + 10)*a(n-7). - Vaclav Kotesovec, Aug 13 2013 MATHEMATICA CoefficientList[Series[4/(2-2x+Sqrt[1-4x]+Sqrt[1-4x^2]), {x, 0, 40}], x] (* Harvey P. Dale, May 12 2011 *) PROG (PARI) x='x+O('x^44) /* that many terms */ gf=4/(2-2*x+sqrt(1-4*x)+sqrt(1-4*x^2)); Vec(gf) /* show terms */ /* Joerg Arndt, Apr 20 2011 */ CROSSREFS Sequence in context: A049143 A089404 A006123 * A049401 A294672 A239077 Adjacent sequences:  A006248 A006249 A006250 * A006252 A006253 A006254 KEYWORD nonn,nice,easy AUTHOR EXTENSIONS More terms from James A. Sellers, Aug 21 2000 STATUS approved

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Last modified November 28 07:44 EST 2020. Contains 338702 sequences. (Running on oeis4.)