A202630
G.f.: exp( Sum_{n>=1} (3^n + A(x))^n * x^n/n ).
Original entry on oeis.org
1, 4, 62, 7646, 11346032, 173032723944, 25223251091617644, 34295314615208803660344, 429734276354140075492905291038, 49292144933883713910495181570024546094, 51546480948489890934875222750204184228031911158
Offset: 0
G.f.: A(x) = 1 + 4*x + 62*x^2 + 7646*x^3 + 11346032*x^4 + 173032723944*x^5 +...
where
log(A(x)) = (3 + A(x))*x + (3^2 + A(x))^2*x^2/2 + (3^3 + A(x))^3*x^3/3 + (3^4 + A(x))^4*x^4/4 +...
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{a(n)=local(A=1+x);for(i=1,n,A=exp(sum(m=1,n,(3^m+A+x*O(x^n))^m*x^m/m)));polcoeff(A,n)}
A185385
G.f. satisfies: A(x) = exp( Sum_{n>=1} (2*A(x) - (-1)^n)^n * x^n/n ).
Original entry on oeis.org
1, 3, 11, 61, 381, 2527, 17559, 126265, 931321, 7007035, 53568131, 414929621, 3249392917, 25684315319, 204645707183, 1641910625009, 13253684541553, 107561523423731, 877109999610107, 7183095973808493, 59053492869471661, 487189276030904207, 4032100262853037127
Offset: 0
G.f.: A(x) = 1 + 3*x + 11*x^2 + 61*x^3 + 381*x^4 + 2527*x^5 + 17559*x^6 +...
where
log(A(x)) = (2*A(x) + 1)*x + (2*A(x) - 1)^2*x^2/2 + (2*A(x) + 1)^3*x^3/3 + (2*A(x) - 1)^4*x^4/4 +...
log(A(x)*(1-2*x*A(x))) = 1/(1 + 2*x*A(x))*x + 1/(1 - 2*x*A(x))^2*x^2/2 + 1/(1 + 2*x*A(x))^3*x^3/3 + 1/(1 - 2*x*A(x))^4*x^4/4 +...
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{a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, (2*A-(-1)^m+x*O(x^n))^m*x^m/m))); polcoeff(A, n)}
A202669
G.f. satisfies: A(x) = exp( Sum_{n>=1} (A(x) + (-1)^n)^n * x^n/n ).
Original entry on oeis.org
1, 0, 2, 2, 12, 20, 96, 212, 898, 2354, 9266, 27070, 102094, 319930, 1177838, 3865762, 14050948, 47574460, 171886784, 594572676, 2143957648, 7528825924, 27156892364, 96412294088, 348314869652, 1246689890248, 4513958859208, 16257651642036, 59010423148052, 213586733348928
Offset: 0
G.f.: A(x) = 1 + 2*x^2 + 2*x^3 + 12*x^4 + 20*x^5 + 96*x^6 + 212*x^7 +...
where
log(A(x)) = (A(x) - 1)*x + (A(x) + 1)^2*x^2/2 + (A(x) - 1)^3*x^3/3 + (A(x) + 1)^4*x^4/4 +...
log(A(x)*(1-x*A(x))) = -1/(1 + x*A(x))*x + 1/(1 - x*A(x))^2*x^2/2 - 1/(1 + x*A(x))^3*x^3/3 + 1/(1 - x*A(x))^4*x^4/4 +...
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{a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, (A+(-1)^m+x*O(x^n))^m*x^m/m))); polcoeff(A, n)}
Showing 1-3 of 3 results.