A386449 G.f. A(x) satisfies A(x) = 1/(1 - x - x^4*A'''(x)).

1, 1, 1, 1, 7, 181, 11215, 1368049, 290015209, 98023774645, 49599740115757, 35810914359761065, 35524377449180431975, 46963191178201310535625, 80682726920407341929523811, 176372394085267937467487988481, 481849299958664384125278899595601, 1619977170089211596368385150640702601

Offset: 0

Author

Seiichi Manyama, Jul 22 2025

Keywords

• nonn

Crossrefs

Cf. A075834, A386448, A386450, A386451.

Cf. A385763.

Programs

PARI

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

Formula

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