A186184 Expansion of 1/(1 - x*A002296(x)).

1, 1, 2, 10, 89, 1002, 12592, 168805, 2363241, 34138860, 505042286, 7612594936, 116492572621, 1804984878387, 28260999959595, 446441276449715, 7106718529937710, 113886198966545724

Offset: 0

Author

Vladimir Kruchinin, Feb 14 2011

Keywords

• nonn

Links

• Vaclav Kotesovec, Recurrence of order 7
• Vladimir Kruchinin and D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 [math.CO], 2011-2013.

Crossrefs

Cf. A002296.

Programs

Maple

A186184 := proc(n)
   if n = 0 then
      1;
   else
      add( k/(6*n-5*k)*binomial(7*n-6*k-1,n-k), k=1..n) ;
   end if;
end proc:
seq(A186184(n),n=0..20) ; # R. J. Mathar, Feb 26 2011

Mathematica

Join[{1},Table[Sum[k/(6n-5k) Binomial[7n-6k-1,n-k],{k,n}],{n,30}]] (* Harvey P. Dale, Aug 29 2012 *)

Formula

a(n) = Sum_{k=1..n} (k/(6*n-5*k))*binomial(7*n-6*k-1, n-k), n > 0.