0,8

Definition: take the triangle in A144385, write it as an (infinite) upper triangular square matrix, invert it and transpose it.

J. Y. Choi and J. D. H. Smith, The Tri-restricted Numbers and Powers of Permutation Representations, J. Comb. Math. Comb. Comp. 42 (2002), 113-125.

J. Y. Choi and J. D. H. Smith, On the Unimodality and Combinatorics of the Bessel Numbers, Discrete Math., 264 (2003), 45-53.

J. Y. Choi and J. D. H. Smith, On the combinatorics of multi-restricted numbers, Ars. Com., 75(2005), pp. 44-63.

J. Y. Choi et al., Reciprocity for multirestricted Stirling numbers, J. Combin. Theory 113 A (2006), 1050-1060.

Triangle begins:

1

0 1

0 -1 1

0 2 -3 1

0 -5 11 -6 1

0 10 -45 35 -10 1

0 35 175 -210 85 -15 1

0 -910 -315 1225 -700 175 -21 1

A:= proc(n, k) option remember; if n=k then 1 elif k<n or n<1 then 0 else A(n-1, k-1) +(k-1) *A(n-1, k-2) +(k-1) *(k-2) *A(n-1, k-3)/2 fi end: M:= proc(n) option remember; Matrix(n+1, (i, j)-> A(i-1, j-1))^(-1) end: T:= (n, k)-> M (n+1)[k+1, n+1]: seq (seq (T(n, k), k=0..n), n=0..12); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 23 2009]

For another version of this triangle see A144634.

Columns give A144636-A144639.

Sequence in context: A038554 A100329 A081247 this_sequence A005210 A048994 A132393

Adjacent sequences: A144630 A144631 A144632 this_sequence A144634 A144635 A144636

sign,tabl

N. J. A. Sloane (njas(AT)research.att.com), Jan 21 2009

Corrected and extended by Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 23 2009