A385759 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^4*A'''(x))).

1, 2, 5, 15, 141, 3932, 251717, 31216948, 6680698525, 2271470142438, 1153913665217481, 835435792656039975, 830424340158140342961, 1099482665756962845820704, 1891111018270919721409143729, 4137752010118540256190073466415, 11312615890237585633045672755792789

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

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

Mathematica

terms = 17; A[_] = 0; Do[A[x_] = 1/((1-x)*(1-x*A[x]-x^4*A'''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 09 2025 *)

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, (1+sum(k=1, 3, stirling(3, k, 1)*j^k))*v[j+1]*v[i-j])); v;

Crossrefs

Cf. A321087, A385758, A385760, A385761.

Sequence in context: A266573 A268121 A306794 * A111790 A309115 A248125

Adjacent sequences: A385756 A385757 A385758 * A385760 A385761 A385762

Keyword

nonn

Author

Seiichi Manyama, Jul 09 2025

Status

approved