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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
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
KEYWORD
nonn,nice,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Aug 21 2000
STATUS
approved

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Last modified March 29 07:27 EDT 2024. Contains 371265 sequences. (Running on oeis4.)