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A141753 Main diagonal of A139755, the table of q-derangement numbers of type A. 2
1, 1, 2, 7, 24, 86, 313, 1157, 4325, 16303, 61856, 235917, 903620, 3473381, 13391280, 51761781, 200523644, 778342906, 3026400508, 11785538461, 45959004812, 179444813270, 701422450293, 2744562302533, 10749124666643, 42135320616531 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..26.

FORMULA

a(n) = [q^n] { ([n+1]_q)! * Sum_{m=0..n+1} (-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).

PROG

(PARI) {a(n)=polcoeff(prod(j=1, n+1, (1-q^j)/(1-q))* sum(k=0, n+1, (-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, A141754.

Sequence in context: A297345 A052986 A053368 * A014300 A128086 A131824

Adjacent sequences:  A141750 A141751 A141752 * A141754 A141755 A141756

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 05 2008

STATUS

approved

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Last modified September 23 09:57 EDT 2020. Contains 337298 sequences. (Running on oeis4.)