A352704 G.f. A(x) satisfies: (1 - x*A(x))^5 = 1 - 5*x - x^5*A(x^5).

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

Author

Paul D. Hanna, Mar 29 2022

Keywords

• nonn

Comments

Essentially an unsigned version of A352703 (after dropping the initial term).

Examples

			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).
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A352703, A352702, A352706.

Programs

PARI

{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),", "))

Formula

G.f. A(x) satisfies:

(1) (1 + x*A(-x))^5 = 1 + 5*x + x^5*A(-x^5).

(2) A(x) = (1 - (1 - 5*x - x^5*A(x^5))^(1/5))/x.

(3) A(x)^5 = A(x^5) (mod 5).