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G.f. A(x) satifiessatisfies: (1 - x*A(x))^7 = 1 - 7*x - x^7*A(x^7).

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Paul D. Hanna, <a href="/A352706/b352706.txt">Table of n, a(n) for n = 0..1000</a>

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allocated for Paul D. Hanna

G.f. A(x) satifies: (1 - x*A(x))^7 = 1 - 7*x - x^7*A(x^7).

1, 3, 13, 65, 351, 1989, 11650, 69900, 427167, 2648438, 16612947, 105215448, 671760933, 4318468134, 27926126553, 181520036178, 1185220461867, 7769787812787, 51117085998498, 337373170647840, 2233091755252871, 14819626692452231, 98582852467595847

0,2

Essentially an unsigned version of A352705 (after dropping the initial term).

G.f. A(x) satisfies:

(1) (1 + x*A(-x))^7 = 1 + 7*x + x^7*A(-x^7).

(2) A(x) = (1 - (1 - 7*x - x^7*A(x^7))^(1/7))/x.

(3) A(x)^7 = A(x^7) (mod 7).

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).

(PARI) {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), ", "))

Cf. A352705, A352702, A352704.

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Paul D. Hanna, Mar 29 2022

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allocated for Paul D. Hanna

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