A158108
L.g.f.: exp(Sum_{n>=1} a(n)*x^n/n) = 1 + x*exp(Sum_{n>=1} sigma(n)*a(n)*x^n/n).
Original entry on oeis.org
1, 1, 4, 21, 186, 1366, 19433, 180541, 3083809, 44941136, 895695901, 11809732422, 359749783368, 5445775854961, 140573612743254, 3607678852423757, 119036988031104164, 2273841364845589333, 93765800142590570954
Offset: 1
-
{a(n)=local(A=x+x^2);if(n==0,1,for(i=1,n-1,A=log(1+x*exp(sum(m=1,n,sigma(m)*x^m*polcoeff(A+x*O(x^m),m) )+x*O(x^n))));n*polcoeff(A,n))}
A158257
G.f.: A(x) = exp(Sum_{n>=1} Lucas(n)*L(n)*x^n/n) such that Sum_{n>=1} L(n)*x^n/n = log(1+x*A(x)) where L(n) = A158258(n) and Lucas(n) = A000204(n).
Original entry on oeis.org
1, 1, 2, 7, 44, 458, 7953, 225761, 10470604, 789302962, 96596105976, 19162936947418, 6158621106553275, 3204835468356347519, 2699695571885775547222, 3680716263445262350996413
Offset: 0
G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 44*x^4 + 458*x^5 + 7953*x^6 +...
log(1+x*A(x)) = x + x^2/2 + 4*x^3/3 + 21*x^4/4 + 186*x^5/5 + 2482*x^6/6 +...
log(A(x)) = x + 3*x^2/2 + 16*x^3/3 + 147*x^4/4 + 2046*x^5/5 + 44676*x^6/6 +...
log(A(x)) = x + 3*1*x^2/2 + 4*4*x^3/3 + 7*21*x^4/4 + 11*186*x^5/5 + 18*2482*x^6/6 +...
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{a(n)=local(A=1+x);if(n==0,1,for(i=1,n,A=exp(sum(m=1,n,(fibonacci(m-1)+fibonacci(m+1))*x^m*polcoeff(log(1+x*A+x*O(x^m)),m))+x*O(x^n)));polcoeff(A,n))}
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