A259533 Number of restricted barred preferential arrangements of an n-set having 3 bars in which 3 fixed sections are restricted sections and 1 section is a free section.
1, 4, 18, 94, 582, 4294, 37398, 378214, 4366422, 56697574, 817979478, 12981058534, 224732536662, 4214866778854, 85130743747158, 1842265527790054, 42525237455785302, 1042966136232956134, 27084277306054500438, 742412698554626764774, 21421502369955072576342, 648998599988032588957414
Offset: 0
Links
- Robert Israel, Table of n, a(n) for n = 0..387
- V. Murali, Ordered partitions and finite fuzzy sets, Far East J. Math. Sci.(FJMS), 21(2006), 12-132.
- S. Nkonkobe and V. Murali, A study of a family of generating functions of Nelsen-Schmidt type and some identities on restricted barred preferential arrangements, arXiv:1503.06172 [math.CO], 2015.
Programs
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Maple
S:= series(exp(3*x)/(2-exp(x)),x,31): seq(coeff(S,x,j)*j!, j=0..30); # Robert Israel, Aug 11 2015
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Mathematica
Range[0, 25]! CoefficientList[Series[E^(3 x)/(2 - E^(x)), {x, 0, 25}], x] (* Vincenzo Librandi, Jul 06 2015 *) -
PARI
{ my(x = xx + O(xx^40)); Vec(serlaplace(exp(3*x)/(2-exp(x)))) } \\ Michel Marcus, Jul 06 2015
Formula
E.g.f.: exp(3*x)/(2-exp(x)).
a(n) = 3^n + Sum_{k = 0..n-1} binomial(n,k)*a(k). - Robert Israel, Aug 11 2015
a(n) ~ 4*n! / (log(2))^(n+1). - Vaclav Kotesovec, Sep 27 2017
a(n) = Sum_{k>=0} (k + 3)^n / 2^(k+1). - Ilya Gutkovskiy, Jun 27 2020
a(n) = 8*A000670(n) - (2^n + 2 + 4*0^n). - Seiichi Manyama, Dec 21 2023
Extensions
More terms from Michel Marcus, Jul 06 2015
Comments