A211386 Expansion of 1/((1-2*x)^5*(1-x)).
1, 11, 71, 351, 1471, 5503, 18943, 61183, 187903, 553983, 1579007, 4374527, 11829247, 31326207, 81461247, 208470015, 525991935, 1310457855, 3228041215, 7870611455, 19012780031, 45541752831, 108246597631, 255466668031, 598980165631, 1395931480063, 3235049897983
Offset: 0
Links
- M. H. Albert, M. D. Atkinson, R. Brignall, The enumeration of three pattern classes using monotone grid classes, El. J. Combinat. 19 (3) (2012) P20.
- Harry Crane, Left-right arrangements, set partitions, and pattern avoidance, Australasian Journal of Combinatorics, 61(1) (2015), 57-72.
- Santiago López de Medrano, On the genera of moment-angle manifolds associated to dual-neighborly polytopes, combinatorial formulas and sequences, arXiv:2003.07508 [math.GT], 2020.
- Index entries for linear recurrences with constant coefficients, signature (11,-50,120,-160,112,-32).
Crossrefs
Cf. A003472 (first differences).
Programs
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Mathematica
CoefficientList[Series[1/((1-2x)^5(1-x)),{x,0,30}],x] (* or *) LinearRecurrence[ {11,-50,120,-160,112,-32},{1,11,71,351,1471,5503},30] (* Harvey P. Dale, Mar 02 2015 *) -
PARI
Vec(1/((1-2*x)^5*(1-x))+ O(x^30)) \\ Michel Marcus, Feb 12 2015
Formula
a(n) = 2^n*(24+18*n+23*n^2+6*n^3+n^4)/12-1.
a(0)=1, a(1)=11, a(2)=71, a(3)=351, a(4)=1471, a(5)=5503, a(n)=11*a(n-1)- 50*a(n-2)+ 120*a(n-3)-160*a(n-4)+112*a(n-5)-32*a(n-6). - Harvey P. Dale, Mar 02 2015
Comments