A381029
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x*A(x)^2)^2).
Original entry on oeis.org
1, 1, 3, 16, 113, 955, 9178, 97427, 1121705, 13836694, 181295019, 2507119320, 36416096984, 553461581406, 8774534872463, 144744539399484, 2479088917439527, 44004108702467428, 808171916050540308, 15335535608825061803, 300272362335527090277, 6059534345675248667550
Offset: 0
-
a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n-j+k, j)/(2*n-j+k)*a(n-j, 2*j)));
A381615
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x*A(x)^3)^3).
Original entry on oeis.org
1, 1, 4, 31, 320, 3969, 56080, 876204, 14860614, 270231265, 5223002719, 106613106181, 2287120272173, 51367948203527, 1204141944566399, 29385603693050274, 744943334951904519, 19580887642660810193, 532781828387893449124, 14984377196395037979472
Offset: 0
-
a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n-2*j+k, j)/(3*n-2*j+k)*a(n-j, 3*j)));
A381593
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x) * A(x*A(x)))^2.
Original entry on oeis.org
1, 2, 11, 88, 869, 9876, 124473, 1701630, 24870695, 384795184, 6257294780, 106377162620, 1882982975521, 34593496243070, 657935674477431, 12927331575084846, 261951066040220637, 5466177185459699916, 117315664923801661485, 2586804284853871362408
Offset: 0
-
a(n, k=2) = if(k==0, 0^n, k*sum(j=0, n, binomial(2*n+j+k, j)/(2*n+j+k)*a(n-j, 2*j)));
A381595
G.f. A(x) satisfies A(x) = 1/(1 - x * A(x) * A(x*A(x)))^3.
Original entry on oeis.org
1, 3, 24, 280, 4044, 67365, 1246534, 25051422, 538836147, 12279937669, 294374405652, 7382843258466, 192917842671564, 5235276617405133, 147163222059602313, 4275948043251399950, 128196303568520249238, 3959890522003241945409, 125863828745364900374059
Offset: 0
-
a(n, k=3) = if(k==0, 0^n, k*sum(j=0, n, binomial(3*n+j+k, j)/(3*n+j+k)*a(n-j, 3*j)));
A384622
G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) * A(x*A(x))^5 ).
Original entry on oeis.org
1, 1, 7, 75, 989, 14822, 242833, 4253818, 78573475, 1516124048, 30358711661, 627789264431, 13357722853019, 291611321803145, 6517101781199460, 148833150175812360, 3468184751644757228, 82363850033966966043, 1991430772785525516280, 48980124394583747435367
Offset: 0
-
a(n, k=1) = if(k==0, 0^n, k*sum(j=0, n, binomial(n+j+k, j)/(n+j+k)*a(n-j, 5*j)));
A107588
G.f. satisfies: A(x) = 1 + ( x/A(x) )/A( x/A(x) ).
Original entry on oeis.org
1, 1, -2, 8, -42, 258, -1764, 13070, -103262, 860812, -7516306, 68380986, -645635800, 6307334042, -63602862362, 660771763808, -7061440267362, 77524521343282, -873398761544252, 10087973928531918, -119358929179189278, 1445596845096459108, -17909930113246116338
Offset: 0
-
{a(n)=local(A=1+x+x*O(x^n)); for(k=1,n,A=1+subst(x/A,x,x/A));polcoeff(A,n)}