A307228 G.f.: A(x) = Sum_{n>=0} x^n * (1 - x*A(x)^(2*n))/(1 - x*A(x)^(2*n+1)).

1, 1, 2, 5, 16, 61, 257, 1153, 5417, 26409, 132812, 686158, 3631067, 19640460, 108424399, 610258791, 3499651848, 20440783169, 121582541298, 736487557803, 4544246421424, 28568504387240, 183061785390324, 1196078847263321, 7971446793975467, 54209318856500848, 376255007650512109, 2665826229768567542, 19281603508757622222, 142358996361189954577, 1072692257581758640368

Offset

0,3

Links

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 5*x^3 + 16*x^4 + 61*x^5 + 257*x^6 + 1153*x^7 + 5417*x^8 + 26409*x^9 + 132812*x^10 + 686158*x^11 + 3631067*x^12 + ...
such that A = A(x) satisfies
A(x) = (1-x)/(1-x*A) + x*(1-x*A^2)/(1-x*A^3) + x^2*(1-x*A^4)/(1-x*A^5) + x^3*(1-x*A^6)/(1-x*A^7) + x^4*(1-x*A^8)/(1-x*A^9) + x^5*(1-x*A^10)/(1-x*A^11) + ...

Mathematica

m = 31; A[_] = 1;
Do[A[x_] = Sum[x^n (1 - x A[x]^(2n))/(1 - x A[x]^(2n + 1)), {n, 0, k}] + O[x]^k, {k, 1, m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Oct 01 2019 *)

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A = Vec( sum(n=0, #A, x^n * (1 - x*Ser(A)^(2*n))/(1 - x*Ser(A)^(2*n+1)) ) )); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A009736 A349458 A370797 * A104858 A351143 A303058

Adjacent sequences: A307225 A307226 A307227 * A307229 A307230 A307231

Keyword

nonn

Author

Paul D. Hanna, Mar 29 2019

Status

approved