A384831 G.f. A(x) satisfies x + x^2 = A(A(x)) - A(A(A(x)))^2.

1, 1, 2, 11, 64, 446, 3420, 28428, 252072, 2360784, 23187228, 237586156, 2529557212, 27898101068, 317939375512, 3736715692256, 45216913769794, 562576653920012, 7188297232200600, 94231521967695334, 1266217030228294392, 17426887813843435996, 245483608643275477496, 3536990534237805030068

Offset

1,3

Links

Paul D. Hanna, Table of n, a(n) for n = 1..500

Example

G.f.: A(x) = x + x^2 + 2*x^3 + 11*x^4 + 64*x^5 + 446*x^6 + 3420*x^7 + 28428*x^8 + 252072*x^9 + 2360784*x^10 + 23187228*x^11 + 237586156*x^12 + ...
RELATED SERIES.
A(A(x)) = x + 2*x^2 + 6*x^3 + 33*x^4 + 216*x^5 + 1612*x^6 + 13204*x^7 + 116272*x^8 + 1086394*x^9 + 10675146*x^10 + ...
A(A(A(x))) = x + 3*x^2 + 12*x^3 + 72*x^4 + 518*x^5 + 4184*x^6 + 36776*x^7 + 345365*x^8 + 3424756*x^9 + 35575824*x^10 + ...
A(A(A(x)))^2 = x^2 + 6*x^3 + 33*x^4 + 216*x^5 + 1612*x^6 + 13204*x^7 + 116272*x^8 + ...

Prog

(PARI) {a(n) = my(A, V=[0, 1, 1]); for(i=1, n, V=concat(V, 0); A = Ser(V);
V[#V] = polcoef(x + x^2 - subst(A, x, A) + subst(A, x, subst(A, x, A))^2, #V-1)/2 ); V[n+1]}
for(n=1, 50, print1(a(n), ", "))

Crossrefs

Sequence in context: A382918 A349023 A001565 * A357845 A199412 A074613

Adjacent sequences: A384828 A384829 A384830 * A384832 A384833 A384834

Keyword

nonn

Author

Paul D. Hanna, Jun 29 2025

Status

approved