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A118023
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Column 0 of triangle A118022, where the matrix square of A118022 shifts each column up 1 row, dropping the main diagonal of powers of 2.
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1
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1, 1, 3, 19, 243, 6227, 319251, 32737427, 6714170259, 2754046149011, 2259333156408723, 3706972573115098515, 12164337831474297132435, 79833941280970262512121235, 1047892334589811621056371520915
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OFFSET
| 0,3
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FORMULA
| G.f.: 1 = Sum_{n>=0} a(n)*x^n*prod_{k=0, n} (1-2^k*x) with a(0)=1.
a(n)=2^(n*(n-1)/2)*b(n) where b(0)=1 and b(n)=sum(i=0,n-1,b(i)*b(n-1-i)/2^i) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 25 2006
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EXAMPLE
| 1 = (1-x) + 1*x*(1-x)*(1-2*x) + 3*x^2*(1-x)*(1-2*x)*(1-4*x)
+ 19*x^3*(1-x)*(1-2*x)*(1-4*x)*(1-8*x)
+ 243*x^4*(1-x)*(1-2*x)*(1-4*x)*(1-8*x)*(1-16*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=0, k, 1-2^j*x+x*O(x^n))), n))}
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CROSSREFS
| Cf. A118022.
Sequence in context: A001929 A157675 A135754 * A054590 A069344 A173799
Adjacent sequences: A118020 A118021 A118022 * A118024 A118025 A118026
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Apr 10 2006
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