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A236406
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Triangle read by rows: number of (1-2-3)-avoiding permutations on n letters with k peaks.
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2
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1, 1, 2, 3, 2, 4, 10, 5, 32, 5, 6, 84, 42, 7, 198, 210, 14, 8, 438, 816, 168, 9, 932, 2727, 1152, 42, 10, 1936, 8250, 5940, 660, 11, 3962, 23276, 25630, 5775, 132, 12, 8034, 62400, 97812, 37180, 2574, 13, 16200, 160953, 341224, 196625, 27456, 429, 14, 32556, 402906, 1111656, 905086, 212212, 10010
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OFFSET
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0,3
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COMMENTS
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This is a convolution of A091156 with itself (see the Pudwell link below).
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LINKS
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FORMULA
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G.f.: G(q,z) = - (-2z^3q^2+4z^3q-2z^3-2z^2q+2z^2-1+sqrt(-4z^2q+4z^2-4z+1))/(2z(zq-z+1)^2). (See the Pudwell link above.)
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EXAMPLE
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Triangle begins:
1;
1;
2;
3, 2;
4, 10;
5, 32, 5;
6, 84, 42;
7, 198, 210, 14;
8, 438, 816, 168;
9, 932, 2727, 1152, 42;
10, 1936, 8250, 5940, 660;
...
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MATHEMATICA
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m = maxExponent = 15;
G = -(-2 z^3 q^2 + 4z^3 q - 2z^3 - 2z^2 q + 2z^2 - 1 + Sqrt[-4z^2 q + 4z^2 - 4z + 1])/(2z (z q - z + 1)^2);
CoefficientList[# + O[q]^m, q]& /@ CoefficientList[G + O[z]^m, z]// Flatten (* Jean-François Alcover, Aug 06 2018 *)
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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