1,3

P. Curtz, Integration numerique des systemes differentiels a conditions initiales. Note no. 12 du Centre de Calcul Scientifique de l'Armement, 1969, 135 pages, p. 61. Available from Centre d'Electronique de L'Armement, 35170 Bruz, France, or INRIA, Projets Algorithmes, 78150 Rocquencourt.

P. Curtz, Gazette des Mathematiciens, 1992, no. 52, p. 44.

P. Flajolet, X. Gourdon and B. Salvy, Gazette des Mathematiciens, 1993, no. 55, pp. 67-78.

E.g.f. for k-th column (k>=1): log(1+x)^k. For further formulae see the references.

First seven rows of T are

[ 1 ]

[ -1, 2 ]

[ 2, -6, 6 ]

[ -6, 22, -36, 24 ]

[ 24, -100, 210, -240, 120 ]

[ -120, 548, -1350, 2040, -1800, 720 ]

[ 720, -3528, 9744, -17640, 21000, -15120, 5040 ]

(MAGMA) m:=21; T:=[ [ Factorial(k)*StirlingFirst(j, k): k in [1..j] ]: j in [1..m] ]; [ &+[ T[j-k+1][k]: k in [1..(j+1) div 2] ]: j in [1..m] ]; /* Klaus Brockhaus, Jun 03 2007 */

Cf. A048594 (T read by rows), A075181 (T unsigned with rows read backwards), A006252 (row sums of T), A000142 (main diagonal of T), A001286 (unsigned first subdiagonal of T). Unsigned values of second through sixth column of T are in A052517, A052748, A052753, A052767, A052779 resp.

Sequence in context: A109499 A124006 A034716 this_sequence A065525 A053454 A125528

Adjacent sequences: A129838 A129839 A129840 this_sequence A129842 A129843 A129844

sign

Paul Curtz (bpcrtz(AT)free.fr), May 22 2007

Edited and extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jun 03 2007