A192406
Main diagonal of square array A192404, with a(0)=1.
Original entry on oeis.org
1, 1, 2, 14, 114, 1131, 12393, 146712, 1838094, 24088842, 327526513, 4593918125, 66198455671, 977113573208, 14741071612583, 226941948201964, 3561383719180100, 56926946565867437, 926444637518092848, 15347533201937448776, 258809102457332568964
Offset: 0
G.f.: A(x) = 1 + x + 2*x^2 + 14*x^3 + 114*x^4 + 1131*x^5 + 12393*x^6 +...
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{a(n)=local(A=1+x*y);for(i=1,n,A=1+sum(m=1,n,x^m*y*A^m/(1-y*A^(2*m)+x*O(x^n)+y*O(y^n))));polcoeff(polcoeff(A,n,x),n,y)}
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{a(n)=local(A=1+x*y);for(i=1,n,A=1+sum(m=1,n,y^m*x*A^(2*m-1)/(1-x*A^(2*m-1)+x*O(x^n)+y*O(y^n))));polcoeff(polcoeff(A,n,y),n,x)}
A192407
A diagonal of square array A192404.
Original entry on oeis.org
1, 4, 31, 291, 3092, 35839, 441925, 5721008, 77009425, 1071034612, 15319883964, 224628789200, 3368096726910, 51552652046550, 804490751228163, 12788591015038781, 206977224029107906, 3409582505289727239, 57165456138722305360
Offset: 1
G.f.: A(x) = x + 4*x^2 + 31*x^3 + 291*x^4 + 3092*x^5 + 35839*x^6 +...
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{a(n)=local(A=x*y);for(i=1,n+1,A=1+sum(m=1,n+1,x^m*y*A^m/(1-y*A^(2*m)+x*O(x^n)+y*O(y^n))));polcoeff(polcoeff(A,n+1,x),n,y)}
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{a(n)=local(A=x*y);for(i=1,n+1,A=1+sum(m=1,n+1,y^m*x*A^(2*m-1)/(1-x*A^(2*m-1)+x*O(x^n)+y*O(y^n))));polcoeff(polcoeff(A,n,y),n+1,x)}
A192405
G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^(n+1) * A(x)^n/(1 - x*A(x)^(2*n)).
Original entry on oeis.org
1, 0, 1, 2, 4, 11, 33, 99, 310, 1016, 3413, 11682, 40751, 144476, 519013, 1886311, 6928012, 25684055, 96020957, 361742039, 1372442092, 5241062187, 20136335035, 77806111700, 302259125863, 1180207733657, 4630733662020, 18254415188073, 72283753111667
Offset: 0
G.f.: A(x) = 1 + x^2 + 2*x^3 + 4*x^4 + 11*x^5 + 33*x^6 + 99*x^7 +...
which satisfies the following relations:
A(x) = 1 + x^2*A(x)/(1-x*A(x)^2) + x^3*A(x)^2/(1-x*A(x)^4) + x^4*A(x)^3/(1-x*A(x)^6) +...
A(x) = 1 + x^2*A(x)/(1-x*A(x)) + x^3*A(x)^3/(1-x*A(x)^3) + x^4*A(x)^5/(1-x*A(x)^5) +...
A(x) = 1 + x^2*A(x) + x^3*A(x)^3*(1 + 1/A(x)) + x^4*A(x)^6*(1 + 1/A(x) + 1/A(x)^3) + x^5*A(x)^10*(1 + 1/A(x) + 1/A(x)^3 + 1/A(x)^6) +...
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{a(n)=local(A=1+x^2);for(i=1,n,A=1+x*sum(m=1,n,x^m*A^m/(1-x*A^(2*m)+x*O(x^n))));polcoeff(A,n)}
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{a(n)=local(A=1+x^2);for(i=1,n,A=1+x*sum(m=1,n,x^m*A^(2*m-1)/(1-x*A^(2*m-1)+x*O(x^n))));polcoeff(A,n)}
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{a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^(m+1)*A^(m*(m+1)/2)*sum(k=0,m-1,(A+x*O(x^n))^(-k*(k+1)/2) ) ) );polcoeff(A,n)}
Showing 1-3 of 3 results.
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