A385760 G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^5*A''''(x))).

1, 2, 5, 15, 51, 1412, 175067, 63725638, 53784616915, 90573359145678, 274256185472187231, 1383348290257488337035, 10961652126528967555229301, 130268275255842369871718355444, 2235924687457083597476492688851325, 53724798520519979444347750309693062183

Offset: 0

Author

Seiichi Manyama, Jul 09 2025

Keywords

• nonn

Crossrefs

Cf. A321087, A385758, A385759, A385761.

Programs

Mathematica

terms = 16; A[] = 0; Do[A[x] = 1/((1-x)*(1-x*A[x]-x^5*A''''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 09 2025 *)

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, 4, stirling(4, k, 1)*j^k))*v[j+1]*v[i-j])); v;

Formula

a(n) = 1 + Sum_{k=0..n-1} (1 - 6*k + 11*k^2 - 6*k^3 + k^4) * a(k) * a(n-1-k).