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A102917
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Column 0 of triangle A102916.
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3
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1, 1, 1, 3, 7, 36, 139, 1036, 5711, 56355, 408354, 5045370, 45605881, 679409158, 7390305396, 129195427716, 1647470410551, 33114233390505, 485292763088275, 11038606786054201, 183049273155939442, 4652371578279864792
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Also equals the interleaving of A082162 with A102921, which equal column 0 of triangle A102098 and its matrix square (A102920), respectively.
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FORMULA
| G.f.: 1 = Sum_{n>=0}(a(2*n)+a(2*n+1)*x)*x^(2*n)*Product_{k=1..n+1}(1-k*x) where a(2*n)=A082162(n) and a(2*n+1)=A102921(n).
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EXAMPLE
| 1 = 1*(1-x) + 1*x*(1-x) + 1*x^2*(1-x)(1-2x) + 3*x^3*(1-x)(1-2x)
+ 7*x^4*(1-x)(1-2x)(1-3x) + 36*x^5*(1-x)(1-2x)(1-3x)
+ 139*x^6*(1-x)(1-2x)(1-3x)(1-4x) + 1036*x^7*(1-x)(1-2x)(1-3x)(1-4x) + ...
+ A082162(n)*x^(2n)*(1-x)(1-2x)*..*(1-(n+1)x)
+ A102921(n)*x^(2n+1)*(1-x)(1-2x)*..*(1-(n+1)x) + ...
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PROG
| (PARI) {a(n)=if(n==0, 1, polcoeff(1-sum(k=0, n-1, a(k)*x^k*prod(j=1, k\2+1, 1-j*x+x*O(x^n))), n))}
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CROSSREFS
| Cf. A102916, A082162, A102921, A102098, A102920.
Sequence in context: A063042 A108505 A047158 * A156465 A049366 A081010
Adjacent sequences: A102914 A102915 A102916 * A102918 A102919 A102920
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 21 2005
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