|
Search: id:A054458
|
|
| |
|
| 1, 3, 1, 7, 6, 1, 17, 23, 9, 1, 41, 76, 48, 12, 1, 99, 233, 204, 82, 15, 1, 239, 682, 765, 428, 125, 18, 1, 577, 1935, 2649, 1907, 775, 177, 21, 1, 1393, 5368, 8680, 7656, 4010, 1272, 238, 24, 1, 3363, 14641, 27312, 28548, 18358, 7506, 1946, 308, 27, 1, 8119
(list; table; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
In the language of the Shapiro et al. reference (given in A053121) such a lower triangular (ordinary) convolution array, considered as a matrix, belongs to the Bell-subgroup of the Riordan-group.
The G.f. for the row polynomials p(n,x) (increasing powers of x) is LPell(z)/(1-x*z*LPell(z)) with LPell(z) given in 'Formula'.
Column sequences are A001333(n+1), A054459(n), A054460(n) for m=0..2.
|
|
FORMULA
|
a(n, m) := ((n-m+1)*a(n, m-1) + (2n-m)*a(n-1, m-1) + (n-1)*a(n-2, m-1))/(4*m), n >= m >= 1; a(n, 0)= A001333(n+1); a(n, m) := 0 if n<m.
G.f. for column m: LPell(x)*(x*LPell(x))^m, m >= 0, with LPell(x)= (1+x)/(1-2*x-x^2) = g.f. for A001333(n+1).
|
|
EXAMPLE
|
{1}; {3,1}; {7,6,1}; {17,23,9,1};...
Fourth row polynomial (n=3): p(3,x)= 17+23*x+9*x^2+x^3
|
|
CROSSREFS
|
Cf. A002203(n+1)/2. Row sums: A055099(n).
Adjacent sequences: A054455 A054456 A054457 this_sequence A054459 A054460 A054461
Sequence in context: A101624 A110441 A111806 this_sequence A110168 A046913 A118228
|
|
KEYWORD
|
easy,nonn,tabl
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 26 2000
|
|
|
Search completed in 0.005 seconds
|
