A091500 Convergent of rows in triangle A091499, in which A091499(n,k) equals the k-th term of the convolution of the two prior rows indexed by (n-k) and (k-1).

1, 1, 2, 4, 9, 20, 47, 113, 275, 676, 1685, 4271, 10843, 27801, 71611, 185795, 484551, 1269717, 3335594, 8806077, 23311686, 61929281, 165062249, 440951151, 1181040770, 3170467624, 8528882846, 22986648032, 62085549929, 167970076540

Offset

0,3

Comments

a(n) equals the n-th term of the convolution of row (n-1) of A091499 with the first n terms of this sequence. Convergent term a(n) first occurs in column n of triangle A091499 in row n*(n+1)/2.

Links

Table of n, a(n) for n=0..29.

Formula

a(n) = A091499(n*(n+1)/2, n). a(n) = Sum A091499(n-1, k)*a(n-1-k) {k=0..n-1} for n>0, with a(0)=1.

Example

a(6) = 47 = (1)*20+(1)*9+(2)*4+(3)*2+(3)*1+(1)*1 since a(6) equals the 6th term of the convolution of row 6 of A091499, {1,1,2,3,3,1}, with the first 6 terms of this sequence, {1,1,2,4,9,20}.

Crossrefs

Cf. A091499, A091501.

Sequence in context: A036721 A014267 A089405 * A370718 A318799 A318852

Adjacent sequences: A091497 A091498 A091499 * A091501 A091502 A091503

Keyword

nonn

Author

Paul D. Hanna, Jan 16 2004

Status

approved