A322626 G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * (n - A(x)^n)^n.

1, 1, 4, 31, 362, 5567, 104229, 2268586, 55817457, 1524956611, 45699911560, 1489007130546, 52390324106713, 1979726546053502, 79978929224189504, 3440756672193895992, 157085559415640319126, 7587124626671398460006, 386598739562989187413005, 20728976430148069600767400, 1166849728839227202686314988

Offset

0,3

Links

Paul D. Hanna, Table of n, a(n) for n = 0..200

Formula

a(n) ~ c * n^(n+1), where c = 0.6410371541108... - Vaclav Kotesovec, Aug 11 2021

Example

G.f.: A(x) = 1 + x + 4*x^2 + 31*x^3 + 362*x^4 + 5567*x^5 + 104229*x^6 + 2268586*x^7 + 55817457*x^8 + 1524956611*x^9 + 45699911560*x^10 + ...
such that
1 = 1 + x*(1 - A(x)) + x^2*(2 - A(x)^2)^2 + x^3*(3 - A(x)^3)^3 + x^4*(4 - A(x)^4)^4 + x^5*(5 - A(x)^5)^5 + x^6*(6 - A(x)^6)^6 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0); A[#A] = Vec(sum(m=0, #A, x^m*(m - Ser(A)^m)^m))[#A+1]); A[n+1]}
for(n=0, 25, print1(a(n), ", "))

Crossrefs

Sequence in context: A086677 A368237 A016036 * A000314 A128709 A138860

Adjacent sequences: A322623 A322624 A322625 * A322627 A322628 A322629

Keyword

nonn

Author

Paul D. Hanna, Jan 28 2019

Status

approved