A352703 G.f. A(x) satisfies: A(x)^5 = A(x^5) + 5*x.

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

0,3

Comments

Not the same as A106223 or A196345.

Links

Table of n, a(n) for n=0..25.

Example

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 + ...

Prog

(PARI) {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), ", "))

Crossrefs

Cf. A107092, A352704, A352705.

Sequence in context: A374554 A106223 A196345 * A352704 A257561 A150203

Adjacent sequences: A352700 A352701 A352702 * A352704 A352705 A352706

Keyword

sign

Author

Paul D. Hanna, Mar 29 2022

Status

approved