|
Search: id:A080248
|
|
|
| A080248 |
|
Stirling-like number triangle defined by sequence A000217. |
|
+0
2
|
|
| 1, 1, 1, 1, 4, 1, 1, 13, 10, 1, 1, 40, 73, 20, 1, 1, 121, 478, 273, 35, 1, 1, 364, 2989, 3208, 798, 56, 1, 1, 1093, 18298, 35069, 15178, 1974, 84, 1, 1, 3280, 110881, 368988, 262739, 56632, 4326, 120, 1, 1, 9841, 668566, 3800761, 4310073, 1452011, 177760
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Columns include A003462, A016211, A021514. The defining sequence A000217(n)=C(n+1,2) is the sequence of partial sums of the sequence (0,1,2,3,4,....) which defines the Stirling numbers of the second kind A008277.
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 13 2009: (Start)
n-th row = M^n * [1,0,0,0,...], where M = an infinite lower triangular matrix
with (1, 3, 6,...) in the main diagonal and (1, 1, 1,...) in the subdiagonal. (End)
|
|
FORMULA
|
Columns are generated by 1/product{k=1, .., n+1, 1-C(k+1, 2)x}
|
|
EXAMPLE
|
Rows are {1}, {1,1}, {1,4,1}, {1, 13, 10, 1}, {1,40, 73, 20, 1}, ... For example, 73 = 13+6.10, 20 = 10+10.1
|
|
PROGRAM
|
(PARI) T(n, k)=local(s); if(k<0|k>n, 0, forvec(v=vector(n-k, i, [0, k]), s+=prod(i=1, n-k, v[i]*(v[i]+1)/2), 1)); s - Michael Somos Feb 06 2004
|
|
CROSSREFS
|
Cf. A000217, A008277.
Sequence in context: A101275 A039755 A047874 this_sequence A139382 A157180 A146956
Adjacent sequences: A080245 A080246 A080247 this_sequence A080249 A080250 A080251
|
|
KEYWORD
|
easy,nonn,tabl
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Feb 17 2003
|
|
|
Search completed in 0.003 seconds
|
