A210670 Central coefficients of triangle A210658.

1, 3, 21, 193, 2047, 23691, 290447, 3707655, 48759741, 656041801, 8987420549, 124936234413, 1757899936601, 24987199202193, 358268701125657, 5175497417194889, 75254198323775151, 1100534370850391355, 16176618251488501319, 238861285362639306383

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = sum(C(i),i=n..2*n), where the C(n)'s are the Catalan numbers.

Recurrence: a(n+1)=a(n)+C(2n+2)+C(2n+1)-C(n).

Recurrence: (n-1)*n*(2*n+1)*(10*n^3 - 51*n^2 + 86*n - 49)*a(n) = 3*(n-1)*(140*n^5 - 844*n^4 + 1851*n^3 - 1784*n^2 + 701*n - 70)*a(n-1) - 6*(280*n^6 - 2308*n^5 + 7496*n^4 - 12166*n^3 + 10376*n^2 - 4523*n + 875)*a(n-2) + 4*(2*n-5)*(4*n-9)*(4*n-7)*(10*n^3 - 21*n^2 + 14*n - 4)*a(n-3). - Vaclav Kotesovec, Aug 13 2013

a(n) ~ 16^n/(3*sqrt(Pi/2)*n^(3/2)). - Vaclav Kotesovec, Aug 13 2013

Mathematica

Table[Sum[Binomial[2i, i]/(i+1), {i, n, 2n}], {n, 0, 100}]

Prog

(Maxima) makelist(sum(binomial(2*i, i)/(i+1), i, n, 2*n), n, 0, 12);

Crossrefs

Cf. A210658.

Sequence in context: A292361 A369783 A151388 * A193468 A132863 A202826

Adjacent sequences: A210667 A210668 A210669 * A210671 A210672 A210673

Keyword

nonn

Author

Emanuele Munarini, Mar 28 2012

Status

approved