A355082 G.f. A(x) satisfies A(x) = 1 + x * A(4 * x / (1 - x)) / (1 - x).

1, 1, 5, 89, 5949, 1546225, 1591006901, 6526287232201, 106972340665773165, 7011394913950382306529, 1838058207026378316690626149, 1927362102757461997768349891040825, 8083963777926072174628168609626454270621

Offset: 0

Author

Seiichi Manyama, Jun 18 2022

Keywords

• nonn

Crossrefs

Column k=4 of A306245.

Cf. A000110, A126443, A355081.

Programs

PARI

a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, 4^j*binomial(i-1, j)*v[j+1])); v;

Formula

a(0) = 1; a(n) = Sum_{k=0..n-1} 4^k * binomial(n-1,k) * a(k).