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A208676
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G.f.: 1 = Sum_{n>=1} a(n) * x^n*(1-x)^(n+1) / Product_{k=1..n} (1 + (k+1)*x).
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5
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1, 1, 4, 23, 169, 1496, 15400, 180055, 2350867, 33840345, 531707256, 9045486916, 165507986668, 3238945135696, 67470601883224, 1489923969768999, 34753006977085479, 853544188578784147, 22011310309759024484, 594514290559650994575, 16780116115165946427561
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OFFSET
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0,3
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COMMENTS
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Related triangle T=A132623 is generated by sums of matrix powers of itself such that:
T(n,k) = Sum_{j=1..n-k-1} [T^j](n-1,k) with T(n+1,n) = n+1 and T(n,n)=0 for n>=0.
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LINKS
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FORMULA
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EXAMPLE
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1 = 1*(1-x) + 1*x*(1-x)^2/(1+2*x) + 4*x^2*(1-x)^3/((1+2*x)*(1+3*x)) + 23*x^3*(1-x)^4/((1+2*x)*(1+3*x)*(1+4*x)) + 169*x^4*(1-x)^5/((1+2*x)*(1+3*x)*(1+4*x)*(1+5*x)) +...
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PROG
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(PARI) {a(n)=if(n<0, 0, polcoeff(1-sum(k=0, n-1, a(k)*x^k*(1-x)^(k+1)/prod(j=1, k, 1+(j+1)*x+x*O(x^n))), n))}
for(n=0, 20, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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