A171486 Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A033321.

1, 1, 1, 2, 2, 1, 6, 5, 3, 1, 21, 16, 9, 4, 1, 79, 58, 31, 14, 5, 1, 311, 224, 117, 52, 20, 6, 1, 1265, 900, 465, 205, 80, 27, 7, 1, 5275, 3720, 1910, 840, 330, 116, 35, 8, 1, 22431, 15713, 8034, 3532, 1396, 501, 161, 44, 9, 1, 96900, 67522, 34419, 15136, 6015, 2190

Offset

0,4

Comments

Equal to B*A065600 = A171224*B where B = A007318 ; equal to B*A039598*B^(-2).

Links

Table of n, a(n) for n=0..60.

Formula

Sum_{k, 0<=k<=n} T(n,k)*x^k = A117641(n), A033321(n), A007317(n+1), A002212(n+1), A026378(n+1) for x = -1, 0, 1, 2, 3 respectively.

T(n,k) = T(n-1,k-1) + T(n-1,k) + sum_{i, i>=0} T(n-1,k+1+i)*2^i. - Philippe Deléham, Feb 23 2012

Example

Triangle begins :
1
1, 1
2, 2, 1
6, 5, 3, 1
21, 16, 9, 4, 1
79, 58, 31, 14, 5, 1
311, 224, 117, 52, 20, 6, 1

Crossrefs

Cf. A171224, A104259, A091965

Sequence in context: A108074 A189175 A271776 * A127743 A125278 A134558

Adjacent sequences: A171483 A171484 A171485 * A171487 A171488 A171489

Keyword

nonn,tabl

Author

Philippe Deléham, Dec 09 2009

Status

approved