A129579 Main diagonal of triangle A129577.

1, 1, 3, 11, 46, 213, 1075, 5854, 34141, 211974, 1394115, 9670976, 70501776, 538393812, 4294921858, 35702077464, 308575560999, 2767618399029, 25713383197122, 247072773486828, 2451716229465559, 25090920235275889

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

Equals first differences (with offset) of column 0 (A129578) of triangle A129577. Equals partial sums (with offset) of row sums (A129580) of triangle A129577.

a(n) = Sum_{k=0..n-1} a(k)*C(2*n-k-1,n-k-1)*(k+2)/(n+1) for n>0, with a(0)=1; eigensequence of triangle A033184 when the first column is omitted. - Paul D. Hanna, Aug 12 2008

Prog

(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(2*n-k-1, n-k-1)*(k+2)/(n+1)*a(k))) \\ Paul D. Hanna, Aug 12 2008

Crossrefs

Cf. A129577, A129578, A129580.

Cf. A033184. - Paul D. Hanna, Aug 12 2008

Sequence in context: A046996 A248426 A337913 * A030814 A030976 A264416

Adjacent sequences: A129576 A129577 A129578 * A129580 A129581 A129582

Keyword

nonn

Author

Paul D. Hanna, Apr 24 2007

Status

approved