|
Search: id:A059594
|
|
|
| A059594 |
|
Convolution triangle based on A008619 (positive integers repeated). |
|
+0
7
|
|
| 1, 1, 1, 2, 2, 1, 2, 5, 3, 1, 3, 8, 9, 4, 1, 3, 14, 19, 14, 5, 1, 4, 20, 39, 36, 20, 6, 1, 4, 30, 69, 85, 60, 27, 7, 1, 5, 40, 119, 176, 160, 92, 35, 8, 1, 5, 55, 189, 344, 376, 273, 133, 44, 9, 1, 6, 70, 294, 624, 820, 714, 434
(list; table; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
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)= sum(a(n,m)*x^m,m=0..n) is 1/((1-z^2)*(1-z)-x*z).
The column sequences are A008619(n); A006918(n); A038163(n-2), n >= 2; A038164(n-3), n >= 3; A038165(n-4), n >= 4; A038166(n-5), n >= 5; A059595(n-6), n >= 6; A059596(n-7), n >= 7; A059597(n-8), n >= 8; A059598(n-9), n >= 9; A059625(n-10), n >= 10 for m=0..10.
The sequence of row sums is A006054(n+2).
|
|
FORMULA
|
a(n, m) := a(n-1, m)+(-(n-m+1)*a(n, m-1)+3*(n+2*m)*a(n-1, m-1))/(8*m), n >= m >= 1; a(n, 0) := floor((n+2)/2)= A008619(n), n >= 0; a(n, m) := 0 if n<m.
G.f.for column m >= 0: ((x/((1-x^2)*(1-x)))^m)/((1-x^2)*(1-x)).
|
|
EXAMPLE
|
{1}; {1,1}; {2,2,1}; {2,5,3,1};...
Fourth row polynomial (n=3): p(3,x)= 2+5*x+3*x^2+x^3.
|
|
CROSSREFS
|
Sequence in context: A098691 A035364 A143808 this_sequence A125678 A091562 A106585
Adjacent sequences: A059591 A059592 A059593 this_sequence A059595 A059596 A059597
|
|
KEYWORD
|
nonn,easy,tabl
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Feb 02 2001
|
|
|
Search completed in 0.002 seconds
|
