A352704
G.f. A(x) satisfies: (1 - x*A(x))^5 = 1 - 5*x - x^5*A(x^5).
Original entry on oeis.org
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, 5199987220813564
Offset: 0
G.f.: A(x) = 1 + 2*x + 6*x^2 + 21*x^3 + 80*x^4 + 320*x^5 + 1326*x^6 + 5637*x^7 + 24434*x^8 + 107542*x^9 + 479196*x^10 + ...
where
(1 - x*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 + ...
also
(1 - 5*x - x^5*A(x^5))^(1/5) = 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 + ...
which equals 1 - x*A(x).
-
{a(n) = my(A=1+2*x); for(i=1,n,
A = (1 - (1 - 5*x - x^5*subst(A,x,x^5) + x*O(x^(n+1)))^(1/5))/x);
polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))
A352702
G.f. A(x) satisfies: (1 - x*A(x))^3 = 1 - 3*x - x^3*A(x^3).
Original entry on oeis.org
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
G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 9*x^4 + 22*x^5 + 55*x^6 + 142*x^7 + 376*x^8 + 1011*x^9 + 2758*x^10 + 7614*x^11 + ...
where
(1 - x*A(x))^3 = 1 - 3*x - x^3 - x^6 - 2*x^9 - 4*x^12 - 9*x^15 - 22*x^18 - 55*x^21 - 142*x^24 - 376*x^27 - 1011*x^30 + ...
also
(1 - 3*x - x^3*A(x^3))^(1/3) = 1 - x - x^2 - 2*x^3 - 4*x^4 - 9*x^5 - 22*x^6 - 55*x^7 - 142*x^8 - 376*x^9 - 1011*x^10 + ...
which equals 1 - x*A(x).
-
{a(n) = my(A=1+x); for(i=1,n,
A = (1 - (1 - 3*x - x^3*subst(A,x,x^3) + x*O(x^(n+1)))^(1/3))/x);
polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))
A352705
G.f. A(x) satisfies: A(x)^7 = A(x^7) + 7*x.
Original entry on oeis.org
1, 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 + 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 + ...
such that A(x)^7 = A(x^7) + 7*x, as illustrated by:
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 + ...
-
{a(n) = my(A=1+x); for(i=1,n,
A = (subst(A,x,x^7) + 7*x + x*O(x^n))^(1/7));
polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))
Showing 1-3 of 3 results.
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