A363474
G.f. satisfies A(x) = exp( 2 * Sum_{k>=1} (-1)^(k+1) * A(-x^k) * x^k/k ).
Original entry on oeis.org
1, 2, -3, -14, 22, 138, -213, -1536, 2474, 18928, -31451, -248992, 420804, 3416514, -5844716, -48349920, 83503128, 700674606, -1219159874, -10345673158, 18109290380, 155082913608, -272798814028, -2353889042848, 4157686512816, 36104006239798
Offset: 0
-
seq(n) = my(A=1); for(i=1, n, A=exp(2*sum(k=1, i, (-1)^(k+1)*subst(A, x, -x^k)*x^k/k)+x*O(x^n))); Vec(A);
A363475
G.f. satisfies A(x) = exp( 3 * Sum_{k>=1} (-1)^(k+1) * A(-x^k) * x^k/k ).
Original entry on oeis.org
1, 3, -6, -44, 96, 918, -2073, -22278, 52629, 597627, -1451736, -17065641, 42205373, 508415817, -1273766637, -15623442097, 39528583206, 491601500847, -1253383246330, -15759867676416, 40430096479776, 512914242127868, -1322511998532891
Offset: 0
-
seq(n) = my(A=1); for(i=1, n, A=exp(3*sum(k=1, i, (-1)^(k+1)*subst(A, x, -x^k)*x^k/k)+x*O(x^n))); Vec(A);
A307538
G.f. A(x) satisfies: A(x) = x*exp(2*A(-x) + 2*A(-x^3)/3 + 2*A(-x^5)/5 + 2*A(-x^7)/7 + 2*A(-x^9)/9 + ...).
Original entry on oeis.org
0, 1, -2, -2, 10, 14, -86, -126, 858, 1302, -9378, -14606, 108954, 172698, -1319966, -2119118, 16489594, 26731542, -210887998, -344490170, 2747510514, 4515757426, -36336187630, -60023827438, 486540793914, 807121753178, -6582918170714, -10959656342678, 89860260268098
Offset: 0
G.f.: A(x) = x - 2*x^2 - 2*x^3 + 10*x^4 + 14*x^5 - 86*x^6 - 126*x^7 + 858*x^8 + 1302*x^9 - 9378*x^10 - 14606*x^11 + ...
-
terms = 28; A[] = 0; Do[A[x] = x Exp[Sum[2 A[-x^(2 k - 1)]/(2 k - 1), {k, 1, terms}]] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x]
a[n_] := a[n] = SeriesCoefficient[x Product[((1 + x^k)/(1 - x^k))^((-1)^k a[k]), {k, 1, n - 1}], {x, 0, n}]; a[0] = 0; Table[a[n], {n, 0, 28}]
Showing 1-3 of 3 results.