A351633 G.f. A(x) satisfies: 1 = Sum_{n>=0} (-x)^n * A(x)^n * (1 - (-x)^(n+1))^(n+1).

1, 1, 3, 7, 19, 54, 161, 492, 1532, 4843, 15503, 50159, 163782, 539050, 1786432, 5956195, 19965072, 67241547, 227433663, 772217118, 2631085326, 8993020595, 30827136777, 105953214815, 365054019536, 1260611616177, 4362291413002

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 7*x^3 + 19*x^4 + 54*x^5 + 161*x^6 + 492*x^7 + 1532*x^8 + 4843*x^9 + 15503*x^10 + 50159*x^11 + 163782*x^12 + ...
where
1 = (1 + x) - x*A(x)*(1 - x^2)^2 + x^2*A(x)^2*(1 + x^3)^3 - x^3*A(x)^3*(1 - x^4)^4 + x^4*A(x)^4*(1 + x^5)^5 - x^5*A(x)^5*(1 - x^6)^6 + ...

Prog

(PARI) {a(n) = my(A = [1]); for(i=1, n, A=concat(A, 0);
A[#A] = polcoeff( sum(m=0, #A, (-x)^m * Ser(A)^m * (1 - (-x)^(m+1))^(m+1) ), #A) ); H=A; A[n+1]}
for(n=0, 60, print1(a(n), ", "))

Crossrefs

Sequence in context: A078481 A183122 A104522 * A115760 A175533 A183115

Adjacent sequences: A351630 A351631 A351632 * A351634 A351635 A351636

Keyword

nonn

Author

Paul D. Hanna, Feb 15 2022

Status

approved