|
Search: id:A141754
|
|
|
| A141754 |
|
Secondary diagonal of A139755, the table of q-derangement numbers of type A. |
|
+0
3
|
|
| 1, 2, 5, 16, 54, 190, 684, 2505, 9291, 34793, 131277, 498312, 1900862, 7280732, 27983141, 107868939, 416869874, 1614609446, 6265869591, 24358231651, 94837442844, 369755864507, 1443420649734, 5641088964709, 22068939198169
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
FORMULA
|
a(n) = [q^n] { ([n+2]_q)! * Sum_{m=0..n+2} (-1)^m * q^(m(m-1)/2) / ([m]_q)! }; here, the q-factorial of n is denoted by ([n]_q)! = Product_{j=1..n} (1-q^j)/(1-q), with ([0]_q)! = 1.
|
|
PROGRAM
|
(PARI) {a(n)=polcoeff(prod(j=1, n+2, (1-q^j)/(1-q))* sum(k=0, n+2, (-1)^k*q^(k*(k-1)/2)/if(k==0, 1, prod(j=1, k, (1-q^j)/(1-q)))), n, q)}
|
|
CROSSREFS
|
Cf. A139755, A141753.
Adjacent sequences: A141751 A141752 A141753 this_sequence A141755 A141756 A141757
Sequence in context: A081126 A006191 A120899 this_sequence A052836 A108526 A051960
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Jul 05 2008
|
|
|
Search completed in 0.002 seconds
|
