A107092
G.f. A(x) satisfies A(x)^3 = A(x^3) + 3*x.
Original entry on oeis.org
1, 1, -1, 2, -4, 9, -22, 55, -142, 376, -1011, 2758, -7614, 21220, -59630, 168759, -480533, 1375676, -3957075, 11430582, -33144264, 96434321, -281447954, 823734157, -2417092933, 7109265120, -20955593252, 61893804180, -183148075432, 542885589115, -1611809502764, 4792612539375
Offset: 0
A(x)^3 = 1 + 3*x + x^3 - x^6 + 2*x^9 - 4*x^12 + 9*x^15 - 22*x^18 +...
A(x^3) = 1 + x^3 - x^6 + 2*x^9 - 4*x^12 + 9*x^15 - 22*x^18+...
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{a(n)=local(A=1+x);for(i=1,n,A=(subst(A,x,x^3)+3*x+x*O(x^n))^(1/3)); polcoeff(A,n,x)}
A352703
G.f. A(x) satisfies: A(x)^5 = A(x^5) + 5*x.
Original entry on oeis.org
1, 1, -2, 6, -21, 80, -320, 1326, -5637, 24434, -107542, 479196, -2157045, 9792702, -44780606, 206055346, -953305632, 4431463863, -20686696920, 96931500840, -455722378776, 2149086843549, -10162544469252, 48176923330632, -228913129263389, 1089973058779915
Offset: 0
G.f.: A(x) = 1 + x - 2*x^2 + 6*x^3 - 21*x^4 + 80*x^5 - 320*x^6 + 1326*x^7 - 5637*x^8 + 24434*x^9 - 107542*x^10 + 479196*x^11 + ...
such that A(x)^5 = A(x^5) + 5*x, as illustrated by:
A(x)^5 = 1 + 5*x + x^5 - 2*x^10 + 6*x^15 - 21*x^20 + 80*x^25 - 320*x^30 + 1326*x^35 - 5637*x^40 + 24434*x^45 - 107542*x^50 + ...
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{a(n) = my(A=1+x); for(i=0,n\5,
A = (subst(A,x,x^5) + 5*x + x*O(x^(5*n)))^(1/5));
polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))
A352706
G.f. A(x) satisfies: (1 - x*A(x))^7 = 1 - 7*x - x^7*A(x^7).
Original entry on oeis.org
1, 3, 13, 65, 351, 1989, 11650, 69900, 427167, 2648438, 16612947, 105215448, 671760933, 4318468134, 27926126553, 181520036178, 1185220461867, 7769787812787, 51117085998498, 337373170647840, 2233091755252871, 14819626692452231, 98582852467595847
Offset: 0
G.f.: A(x) = 1 + 3*x + 13*x^2 + 65*x^3 + 351*x^4 + 1989*x^5 + 11650*x^6 + 69900*x^7 + 427167*x^8 + 2648438*x^9 + 16612947*x^10 + ...
where
(1 - x*A(x))^7 = 1 - 7*x - x^7 - 3*x^14 - 13*x^21 - 65*x^28 - 351*x^35 - 1989*x^42 - 11650*x^49 - 69900*x^56 - 427167*x^63 - 2648438*x^70 + ...
also
(1 - 7*x - x^7*A(x^7))^(1/7) = 1 - x - 3*x^2 - 13*x^3 - 65*x^4 - 351*x^5 - 1989*x^6 - 11650*x^7 - 69900*x^8 - 427167*x^9 - 2648438*x^10 + ...
which equals 1 - x*A(x).
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{a(n) = my(A=1+3*x); for(i=1,n,
A = (1 - (1 - 7*x - x^7*subst(A,x,x^7) + x*O(x^(n+1)))^(1/7))/x);
polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))
Showing 1-3 of 3 results.
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