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A129579
Main diagonal of triangle A129577.
3
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
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. A033184. - Paul D. Hanna, Aug 12 2008
Sequence in context: A046996 A248426 A337913 * A030814 A030976 A264416
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 24 2007
STATUS
approved