A394802 - OEIS

A394802

G.f. A(x) satisfies A(x) = 1 - x^4 * d/dx log(1 - x*A(x)).

1, 0, 0, 0, 1, 1, 1, 1, 6, 13, 22, 33, 91, 236, 518, 997, 2328, 5986, 14676, 32817, 77045, 195385, 500537, 1222296, 2993677, 7653702, 20059267, 51655893, 132106706, 344907954, 921230101, 2456997586, 6517923856, 17452808288, 47527956033, 130136519697, 355757503817

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OFFSET

0,9

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

G.f. A(x) satisfies A(x) = 1 - x*A(x) + x*A(x)^2 + x^4*A(x) + x^5*d/dx A(x).

a(0) = 1, a(1) = a(2) = a(3) = 0; a(n) = (n-3)*a(n-4) + Sum_{k=1..n-1} a(k) * a(n-1-k).

a(n) = A394800(n) - Sum_{k=0..n-1} a(k) * A394800(n-1-k).

G.f.: B(x)/(1+x*B(x)), where B(x) is the g.f. of A394800.

MATHEMATICA

terms = 37; A[_] = 1; Do[A[x_] = 1-x^4 * D[Log[1-x*A[x]], x]+O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Apr 02 2026 *)