A385840 a(n) = 1 + Sum_{k=0..n-1} k^2 * a(k) * a(n-1-k).

1, 1, 2, 10, 101, 1733, 45303, 1680907, 84166419, 5475072843, 449157456364, 45377436182152, 5537042709272831, 802969519178558759, 136516626968319610486, 26895468447194766859402, 6078661245454015521843883, 1562271796018872884111521763, 453071380100390505646644605866

Offset

0,3

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^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, j^2*v[j+1]*v[i-j])); v;

Crossrefs

Cf. A143917, A385841, A385842, A385843.

Cf. A385830, A385835, A385874.

Sequence in context: A228120 A377919 A074109 * A291101 A036336 A379535

Adjacent sequences: A385837 A385838 A385839 * A385841 A385842 A385843

Keyword

nonn

Author

Seiichi Manyama, Jul 09 2025

Status

approved