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A141754 Secondary diagonal of A139755, the table of q-derangement numbers of type A. 2
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; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..25.

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.

PROG

(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.

Sequence in context: A120899 A149960 A149961 * A149962 A149963 A149964

Adjacent sequences:  A141751 A141752 A141753 * A141755 A141756 A141757

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 05 2008

STATUS

approved

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Last modified September 29 11:11 EDT 2020. Contains 337430 sequences. (Running on oeis4.)