A213009
G.f. A(x) satisfies: A(A(x)) = x+x^2 + x*A(A(A(A(x)))).
Original entry on oeis.org
1, 1, 1, 5, 21, 125, 825, 6133, 49925, 439417, 4142945, 41544161, 440710117, 4924691541, 57766255689, 709205703565, 9090541134373, 121389729560633, 1685431945085489, 24289856880005441, 362776874949660485, 5606980244843123077, 89560387072919814553
Offset: 1
G.f.: A(x) = x + x^2 + x^3 + 5*x^4 + 21*x^5 + 125*x^6 + 825*x^7 +...
where
A(A(x)) = x + 2*x^2 + 4*x^3 + 16*x^4 + 80*x^5 + 480*x^6 + 3296*x^7 +...
A(A(A(A(x)))) = x + 4*x^2 + 16*x^3 + 80*x^4 + 480*x^5 + 3296*x^6 +...
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{a(n)=local(A=x+x^2,B=x+2*x^2);for(i=1,n,B=x+x^2+x*subst(B,x,B+x*O(x^n)));
for(i=1,n,A=(A+subst(B,x,serreverse(A+x*O(x^n))))/2);polcoeff(A,n)}
for(n=1,31,print1(a(n),", "))
A215116
G.f. satisfies: A(x) = x + 3*x^2 + x*A(A(A(A(x)))).
Original entry on oeis.org
1, 4, 16, 256, 4864, 111616, 2983936, 89743360, 2970861568, 106768629760, 4125849419776, 170207219286016, 7454572671926272, 345078981839552512, 16822127738969128960, 860944587541763325952, 46137178395559050870784, 2582843669636660403896320, 150735442996358913332346880
Offset: 1
G.f.: A(x) = x + 4*x^2 + 16*x^3 + 256*x^4 + 4864*x^5 + 111616*x^6 + 2983936*x^7 +...
where
A(A(A(A(x)))) = x + 16*x^2 + 256*x^3 + 4864*x^4 + 111616*x^5 + 2983936*x^6 +...
Related expansions.
Let D(D(D(D(x)))) = A(x), then D(x) is an integer series where:
D(x) = x + x^2 + x^3 + 49*x^4 + 721*x^5 + 17281*x^6 + 452065*x^7 +...
where the coefficients of D(x) are congruent to 1 modulo 48.
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{a(n)=local(A=x+4*x^2); for(i=1,n,A=x+3*x^2+x*subst(A,x,subst(A,x,subst(A,x,A+x*O(x^n))))); polcoeff(A, n)}
for(n=1, 31, print1(a(n), ", "))
A215114
G.f. satisfies: A(x) = x + 2*x^2 + x*A(A(A(x))).
Original entry on oeis.org
1, 3, 9, 81, 891, 11907, 184437, 3199581, 60932007, 1257133527, 27836230041, 656867748537, 16429561047891, 433686821472747, 12038953175046909, 350402975398982133, 10665927632978564895, 338769129913521564735, 11205026468737167058785
Offset: 1
G.f.: A(x) = x + 3*x^2 + 9*x^3 + 81*x^4 + 891*x^5 + 11907*x^6 + 184437*x^7 +...
where
A(A(A(x))) = x + 9*x^2 + 81*x^3 + 891*x^4 + 11907*x^5 + 184437*x^6 +...
Related expansions.
Let C(C(C(x))) = A(x), then C(x) is an integer series where:
C(x) = x + x^2 + x^3 + 19*x^4 + 163*x^5 + 2269*x^6 + 34093*x^7 +...
where the coefficients of C(x) are congruent to 1 modulo 9.
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{a(n)=local(A=x+3*x^2); for(i=1, n, A=x+2*x^2+x*subst(A, x, subst(A, x, A+x*O(x^n)))); polcoeff(A, n)}
for(n=1, 31, print1(a(n), ", "))
A215118
G.f. satisfies: A(x) = x + 4*x^2 + x*A(A(A(A(A(x))))).
Original entry on oeis.org
1, 5, 25, 625, 18125, 628125, 25390625, 1158515625, 58308203125, 3190470703125, 187941103515625, 11832996337890625, 791834056298828125, 56063448811767578125, 4184231129351806640625, 328154000925299072265625, 26970505516268341064453125, 2317475342690856231689453125
Offset: 1
G.f.: A(x) = x + 5*x^2 + 25*x^3 + 625*x^4 + 18125*x^5 + 628125*x^6 + ...
where
A(A(A(A(x)))) = x + 25*x^2 + 625*x^3 + 18125*x^4 + 628125*x^5 + ...
Related expansions.
Let E(E(E(E(E(x))))) = A(x), then E(x) is an integer series where:
E(x) = x + x^2 + x^3 + 101*x^4 + 2301*x^5 + 82601*x^6 + 3287001*x^7 + ...
where the coefficients of E(x) are congruent to 1 modulo 100.
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{a(n) = my(A=x+4*x^2); for(i=1,n,A=x+4*x^2+x*subst(A,x,subst(A,x,subst(A,x,subst(A,x,A+x*O(x^n)))))); polcoef(A, n)}
for(n=1, 31, print1(a(n), ", "))
Showing 1-4 of 4 results.
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