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A294790
Subtract n from partial sums of partial sums of Catalan numbers.
2
1, 2, 5, 13, 35, 99, 295, 920, 2975, 9892, 33605, 116104, 406615, 1440026, 5147877, 18550573, 67310939, 245716095, 901759951, 3325066997, 12312494463, 45766188949, 170702447075, 638698318851, 2396598337951, 9016444758503, 34003644251207, 128524394659915
OFFSET
0,2
LINKS
Christopher Bao, Yunseo Choi, Katelyn Gan, and Owen Zhang, On a Conjecture by Baril, Cerbai, Khalil, and Vajnovszki on Two Restricted Stacks, arXiv:2308.09344 [math.CO], 2023.
Giulio Cerbai, Anders Claesson, and Luca Ferrari, Stack sorting with restricted stacks, arXiv:1907.08142 [cs.DS], 2019.
Giulio Cerbai, Anders Claesson, Luca Ferrari, and Einar Steingrímsson, Sorting with pattern-avoiding stacks: the 132-machine, arXiv:2006.05692 [math.CO], 2020.
Lapo Cioni and Luca Ferrari, Enumerative Results on the Schröder Pattern Poset, In: Dennunzio A., Formenti E., Manzoni L., Porreca A. (eds) Cellular Automata and Discrete Complex Systems, AUTOMATA 2017, Lecture Notes in Computer Science, vol 10248. See p. 65.
FORMULA
a(n) = A014140(n) - n.
MAPLE
a:= proc(n) option remember; `if`(n<3, 1+n^2,
(6*n*a(n-1)-(9*n-3)*a(n-2)+(4*n-2)*a(n-3))/(n+1))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Oct 01 2019
MATHEMATICA
MapIndexed[#1 - First[#2] + 1 &, CoefficientList[Series[1/(1 - x)^2*(1 - Sqrt[1 - 4 x])/(2 x), {x, 0, 27}], x]] (* Michael De Vlieger, Oct 01 2019 *)
CROSSREFS
Cf. A014140. - Michael De Vlieger, Oct 01 2019
Sequence in context: A126221 A376277 A107086 * A234643 A089846 A258450
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Nov 08 2017
STATUS
approved