A380041
E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)^2) )^(1/3).
Original entry on oeis.org
1, 1, 6, 67, 1124, 25325, 718606, 24629395, 990296504, 45718478137, 2383877762810, 138578689119431, 8887132981365508, 623319005140469989, 47465740413056117894, 3900149351529967753435, 343951717449176947732976, 32405206661688405897284849, 3248370338004030319683766642
Offset: 0
A380043
E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)^3) )^(1/3).
Original entry on oeis.org
1, 1, 6, 73, 1364, 34585, 1110406, 43200535, 1975744856, 103892750209, 6176282882570, 409635957376591, 29988473838531748, 2402004132488328433, 208956515057627326094, 19619264794744128427495, 1977503574407863125008816, 212975277029523353673126529, 24408338689788753822318157330
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x/(1+3*x*exp(x)))/x)^(1/3)))
-
a(n) = n!*sum(k=0, n, 3^k*k^(n-k)*binomial(n+1/3, k)/(n-k)!)/(3*n+1);
A380040
E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)) )^(2/3).
Original entry on oeis.org
1, 2, 14, 170, 3000, 69930, 2033212, 70972734, 2894590064, 135164076722, 7113787010100, 416759006663142, 26903080612468744, 1897553477118350922, 145204649027247413996, 11982094054396851014030, 1060673494236770414806752, 100265097180082772515691874, 10080871201186661027182272868
Offset: 0
A380078
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - 3*x*exp(x))^(1/3) ).
Original entry on oeis.org
1, 1, 8, 115, 2484, 72005, 2626846, 115688349, 5974568552, 354154378249, 23704428986010, 1768459611322481, 145525743200753356, 13095070459815108141, 1279226572751177845718, 134827003107939467441845, 15250595677663579282034256, 1842758049329907303778372625
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-3*x*exp(x))^(1/3))/x))
-
a(n) = n!*sum(k=0, n, 3^k*k^(n-k)*binomial(n/3+k+1/3, k)/((n+3*k+1)*(n-k)!));
Showing 1-4 of 4 results.