A213233
G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^10)^4).
Original entry on oeis.org
1, 1, 5, 39, 345, 3512, 38431, 451620, 5587237, 72275004, 968509140, 13361356169, 188704259571, 2716467168169, 39716842554828, 588125693790055, 8800638181341593, 132838773216409675, 2019626662710709088, 30891440565153652705, 474899505740289874276
Offset: 0
G.f.: A(x) = 1 + x + 5*x^2 + 39*x^3 + 345*x^4 + 3512*x^5 + 38431*x^6 +...
Related expansions:
A(x)^10 = 1 + 10*x + 95*x^2 + 960*x^3 + 10095*x^4 + 111212*x^5 +...
1/A(-x*A(x)^10)^4 = 1 + 4*x + 30*x^2 + 256*x^3 + 2605*x^4 + 28484*x^5 +...
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{a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A^4, x, -x*subst(A^10, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
A213227
G.f. satisfies: A(x) = 1/(1 - x/A(-x*A(x)^6)).
Original entry on oeis.org
1, 1, 2, 8, 35, 181, 1042, 6301, 39435, 249744, 1585386, 10027385, 62696192, 385398251, 2322152120, 13727653882, 80274175978, 472701550856, 2883417403654, 18796497074750, 132728456810968, 995480740265410, 7605881152587204, 56821415293287735, 403362682583930224
Offset: 0
G.f.: A(x) = 1 + x + 2*x^2 + 8*x^3 + 35*x^4 + 181*x^5 + 1042*x^6 +...
Related expansions:
A(x)^6 = 1 + 6*x + 27*x^2 + 128*x^3 + 645*x^4 + 3462*x^5 + 19823*x^6 +...
1/A(-x*A(x)^6) = 1 + x + 5*x^2 + 20*x^3 + 108*x^4 + 638*x^5 + 3889*x^6 +...
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{a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1/(1-x/subst(A, x, -x*subst(A^6, x, x+x*O(x^n)))) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
A384896
G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x))^3.
Original entry on oeis.org
1, 1, 3, 0, -23, -51, 27, 920, 5469, 4836, -84822, -515991, -1733406, 2541688, 64653336, 324962160, 800371560, -3164656113, -49575569463, -260541998755, -734864189592, 1794936737274, 39518722602456, 260877913774320, 1122691536976305, 1485180173013631
Offset: 0
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a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-n+2*j+k-1, j-1)*a(n-j, 3*j)/j));
A384897
G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x)^2)^3.
Original entry on oeis.org
1, 1, 3, 3, -8, -81, -462, -1140, 1662, 42210, 341922, 1588428, 3968106, -17035461, -330216303, -2645037192, -15366663001, -56099904270, 42126523152, 2923843607931, 33032055390075, 253102960693959, 1474460670302136, 5496172108115193, -8530990617203547
Offset: 0
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a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-2*n+3*j+k-1, j-1)*a(n-j, 3*j)/j));
A384898
G.f. A(x) satisfies A(x) = 1 + x/A(-x*A(x)^3)^3.
Original entry on oeis.org
1, 1, 3, 6, 10, -39, -546, -3563, -18918, -68472, -47978, 2060310, 25856241, 210422728, 1367033271, 6837535155, 18339297562, -114989342976, -2525856651999, -27658429475813, -235591084478085, -1658029364805855, -9188248947018893, -28582654956147315, 177119046663378954
Offset: 0
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a(n, k=-1) = if(n*k==0, 0^n, (-1)^n*k*sum(j=1, n, binomial(-3*n+4*j+k-1, j-1)*a(n-j, 3*j)/j));
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