A247582 Triangle, read by rows, T(n,k) = (k+1)*Sum_{i=0..n-k} C(k+2*i,i)*C(n-i-1,n-k-i)/(k+i+1).

1, 1, 1, 2, 3, 1, 5, 8, 5, 1, 14, 22, 18, 7, 1, 42, 64, 59, 32, 9, 1, 132, 196, 190, 124, 50, 11, 1, 429, 625, 618, 448, 225, 72, 13, 1, 1430, 2055, 2047, 1576, 910, 370, 98, 15, 1, 4862, 6917, 6908, 5510, 3482, 1664, 567, 128, 17, 1, 16796, 23713, 23703, 19322, 12958, 6924, 2814, 824, 162, 19, 1

Offset

0,4

Links

Table of n, a(n) for n=0..65.

Formula

G.f.: 1/(1-(1-sqrt(1-4*x))/2-y*(x/(1-x))).

Example

1;
1, 1;
2, 3, 1;
5, 8, 5, 1;
14, 22, 18, 7, 1;
42, 64, 59, 32, 9, 1;

Prog

(Maxima) T(n, k):=(k+1)*sum((binomial(k+2*i, i)*binomial(n-i-1, n-k-i))/(k+i+1), i, 0, n-k);

Crossrefs

Cf. A000108 (first column), A014138.

Sequence in context: A242107 A242108 A238941 * A359795 A224652 A271497

Adjacent sequences: A247579 A247580 A247581 * A247583 A247584 A247585

Keyword

nonn,tabl

Author

Vladimir Kruchinin, Apr 21 2015

Status

approved