A385948 a(0) = 1; a(n) = Sum_{k=0..n-1} binomial(k+6,6) * binomial(n-1,k) * a(k) * a(n-1-k).

1, 1, 8, 246, 21750, 4689546, 2197062708, 2046202234224, 3528088593902364, 10627093734265740672, 53295889303479275834616, 427383379745842299684115608, 5294446934064450139154214169992, 98355143996083993836475641916586304, 2669951662594756888115675117287929721248

Offset

0,3

Links

Table of n, a(n) for n=0..14.

Formula

E.g.f. A(x) satisfies A(x) = exp( Sum_{k=0..5} binomial(5,k) * x^(k+1)/(k+1)! * (d^k/dx^k A(x)) ), where (d^0/dx^0 A(x)) = A(x) by convention.

Prog

(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, binomial(j+6, 6)*binomial(i-1, j)*v[j+1]*v[i-j])); v;

Crossrefs

Cf. A000272, A156325, A385945, A385946, A385947.

Cf. A385955.

Sequence in context: A062481 A053089 A090241 * A242196 A316802 A299648

Adjacent sequences: A385945 A385946 A385947 * A385949 A385950 A385951

Keyword

nonn

Author

Seiichi Manyama, Jul 13 2025

Status

approved