A385835 a(n) = 1 + Sum_{k=0..n-1} (1 + k^2) * a(k) * a(n-1-k).

1, 2, 7, 51, 660, 13350, 390886, 15728919, 836469748, 56989647229, 4849599126797, 504709937298467, 63117270187248665, 9344222191368190761, 1616899887657388367640, 323430766605746093449465, 74074314477265886578774322, 19261037812212680097678843345, 5643873902659784713257894768422

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..253

Formula

G.f. A(x) satisfies A(x) = 1/( (1 - x) * ( 1 - x*A(x) - x^2 * (d/dx A(x)) - x^3 * (d^2/dx^2 A(x)) ) ).

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, (1+j^2)*v[j+1]*v[i-j])); v;

Crossrefs

Cf. A321087, A385836, A385837, A385838, A385839.

Cf. A385758.

Sequence in context: A086902 A381940 A265042 * A249754 A224879 A345678

Adjacent sequences: A385832 A385833 A385834 * A385836 A385837 A385838

Keyword

nonn

Author

Seiichi Manyama, Jul 09 2025

Status

approved