A191809
G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^binomial(n+2,3).
Original entry on oeis.org
1, 1, 2, 7, 32, 174, 1071, 7281, 53943, 432555, 3743146, 34934853, 351853883, 3827477399, 44985837602, 570985992828, 7814212692498, 115024461077654, 1815588345261996, 30628743324667923, 550414603283527315, 10503650627005928698
Offset: 0
G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 32*x^4 + 174*x^5 + 1071*x^6 +...
where the g.f. satisfies:
A(x) = 1 + x*A(x) + x^2*A(x)^4 + x^3*A(x)^10 + x^4*A(x)^20 + x^5*A(x)^35 + x^6*A(x)^56 + x^7*A(x)^84 +...+ x^n*A(x)^(n*(n+1)*(n+2)/3!) +...
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{a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^(m*(m+1)*(m+2)/3!)));polcoeff(A,n)}
A191811
G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^binomial(n+4,5).
Original entry on oeis.org
1, 1, 2, 9, 58, 501, 5452, 74211, 1257414, 26480393, 689598502, 21957924255, 844532153323, 38719749230469, 2091808065954023, 131835936103587004, 9607988537163939224, 803620426590302536069, 76622443259122023510169
Offset: 0
G.f.: A(x) = 1 + x + 2*x^2 + 9*x^3 + 58*x^4 + 501*x^5 + 5452*x^6 +...
where the g.f. satisfies:
A(x) = 1 + x*A(x) + x^2*A(x)^6 + x^3*A(x)^21 + x^4*A(x)^56 + x^5*A(x)^126 + x^6*A(x)^252 + x^7*A(x)^462 +...+ x^n*A(x)^(n*(n+1)*(n+2)*(n+3)*(n+4)/5!) +...
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{a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^binomial(m+4,5)));polcoeff(A,n)}
A191812
G.f. satisfies: A(x) = Sum_{n>=0} x^n*A(x)^binomial(n+5,6).
Original entry on oeis.org
1, 1, 2, 10, 74, 782, 10982, 206346, 5142544, 168789842, 7201158787, 391194813232, 26651992683511, 2239377066821882, 229147222941318059, 28241058833042859637, 4149246030879282392144, 720738467750916348374860, 146838784937226592635807695
Offset: 0
G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 74*x^4 + 782*x^5 + 10982*x^6 +...
where the g.f. satisfies:
A(x) = 1 + x*A(x) + x^2*A(x)^7 + x^3*A(x)^28 + x^4*A(x)^84 + x^5*A(x)^210 + x^6*A(x)^462 + x^7*A(x)^924 +...+ x^n*A(x)^(n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)/6!) +...
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{a(n)=local(A=1+x);for(i=1,n,A=1+sum(m=1,n,x^m*(A+x*O(x^n))^binomial(m+5,6)));polcoeff(A,n)}
Showing 1-3 of 3 results.