A301578
G.f. A(x) satisfies: A(x) = Product_{k>=1} (1 + k*x^k*A(x)^k).
Original entry on oeis.org
1, 1, 3, 12, 48, 211, 970, 4594, 22311, 110473, 555561, 2829918, 14570666, 75708835, 396481070, 2090558864, 11089276706, 59135014252, 316836936662, 1704764660218, 9207671377450, 49904141524184, 271325301723223, 1479427708380368, 8088057338101442, 44325245804200151
Offset: 0
G.f. A(x) = 1 + x + 3*x^2 + 12*x^3 + 48*x^4 + 211*x^5 + 970*x^6 + 4594*x^7 + 22311*x^8 + 110473*x^9 + ...
G.f. A(x) satisfies: A(x) = (1 + x*A(x)) * (1 + 2*x^2*A(x)^2) * (1 + 3*x^3*A(x)^3) * (1 + 4*x^4*A(x)^4) * ...
log(A(x)) = x + 5*x^2/2 + 28*x^3/3 + 137*x^4/4 + 726*x^5/5 + 3896*x^6/6 + 21071*x^7/7 + 115089*x^8/8 + ... + A297322(n)*x^n/n + ...
A302288
G.f. A(x) satisfies: A(x) = Product_{k>=1} 1/(1 - k*x^k*A(x)).
Original entry on oeis.org
1, 1, 4, 14, 55, 217, 908, 3864, 16894, 75078, 338862, 1548055, 7147427, 33294790, 156305144, 738753341, 3512431392, 16788169689, 80619590577, 388785776751, 1882063496033, 9142361671588, 44550166132194, 217716111661799, 1066792279046783, 5239947708977474, 25795965431819883
Offset: 0
G.f. A(x) = 1 + x + 4*x^2 + 14*x^3 + 55*x^4 + 217*x^5 + 908*x^6 + 3864*x^7 + 16894*x^8 + 75078*x^9 + 338862*x^10 + ...
G.f. A(x) satisfies: A(x) = 1/((1 - x*A(x)) * (1 - 2*x^2*A(x)) * (1 - 3*x^3*A(x)) * (1 - 4*x^4*A(x)) * ...).
A302289
G.f. A(x) satisfies: A(x) = Product_{k>=1} (1 + k*x^k*A(x)).
Original entry on oeis.org
1, 1, 3, 10, 30, 98, 323, 1083, 3684, 12710, 44272, 155608, 551259, 1965952, 7052990, 25436711, 92168542, 335376653, 1224991077, 4489818110, 16507728007, 60868469848, 225030777305, 833961333273, 3097594423724, 11529400593846, 42996077073284, 160632616725238, 601132116489719, 2253153800577748
Offset: 0
G.f. A(x) = 1 + x + 3*x^2 + 10*x^3 + 30*x^4 + 98*x^5 + 323*x^6 + 1083*x^7 + 3684*x^8 + 12710*x^9 + 44272*x^10 + ...
G.f. A(x) satisfies: A(x) = (1 + x*A(x)) * (1 + 2*x^2*A(x)) * (1 + 3*x^3*A(x)) * (1 + 4*x^4*A(x)) * ...
Showing 1-3 of 3 results.