A186183 Expansion of 1/(1-x*A002295(x)).

1, 1, 2, 9, 68, 646, 6857, 77695, 919642, 11233858, 140544189, 1791614714, 23187320736, 303861373679, 4023883823059, 53762917329659, 723854999871943, 9811154512175468, 133762940465746744, 1833187046654598058, 25239961633188882896

Offset: 0

Author

Vladimir Kruchinin, Feb 14 2011

Keywords

• nonn

Links

• Vaclav Kotesovec, Recurrence of order 6
• Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Programs

Maple

a:= n-> `if` (n=0, 1, add (k/(5*n-4*k) *binomial (6*n-5*k-1, n-k), k=1..n)):
seq (a(n), n=0..30);

PARI

a(n)=max(1,sum(k=1,n, k/(5*n-4*k)*binomial(6*n-5*k-1,n-k)))

Formula

a(n) = Sum_{k=1..n} k/(5*n-4*k) * binomial(6*n-5*k-1,n-k) if n>0; a(0)=1.

a(n) ~ 2^(6*n+4) * 3^(6*n + 9/2) / (51136801 * sqrt(Pi) * n^(3/2) * 5^(5*n - 7/2)). - Vaclav Kotesovec, Sep 22 2024