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 A144108 Eigentriangle based on A052186 (permutations without strong fixed points), row sums = n! 2
 1, 0, 1, 1, 0, 1, 3, 1, 0, 2, 14, 3, 1, 0, 6, 77, 14, 3, 2, 0, 24, 497, 77, 14, 6, 6, 0, 120, 3676, 497, 77, 28, 18, 24, 0, 720, 30677, 3676, 497, 154, 84, 72, 120, 0, 5040, 285335, 30677, 3676, 994, 462, 336, 360, 720, 0, 40320 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Row sums = n!. Sum n-th row terms = rightmost term of next row. Left border = A052186. LINKS FORMULA Eigentriangle by rows, T(n,k) = A052186(n-k)*X; 0<=k<=n; where X = an infinite lower triangular matrix with the factorials shifted to (1, 1, 1, 2, 6, 24,...) in the main diagonal and the rest zeros. The triangle A052186 is composed of A052186 in every column: (1, 0, 1, 3, 14, 77, 497,...). The operations are equivalent to (by rows): termwise products of (n+1) terms of A052186 (reversed) and an equal number of terms in the series: (1, 1, 1, 2, 6, 24, 120,...). EXAMPLE First few rows of the triangle = 1; 0, 1; 1, 0, 1; 3, 1, 0, 2; 14, 3, 1, 0, 6; 77, 14, 3, 2, 0, 24; 497, 77, 14, 6, 6, 0, 120; 3676, 497, 77, 28, 18, 24, 0, 720; 30677, 3676, 497, 154, 84, 72, 120, 0, 5040; 285335, 30677, 3676, 994, 462, 336, 360, 720, 0, 40320; ... Row 3 = (14, 3, 1, 0, 6) = termwise products of (14, 3, 1, 0, 1) and (1, 1, 1, 2, 6) = (14*1, 3*1, 1*1, 0*2, 1*6). CROSSREFS A000142, Cf. A052186 Sequence in context: A194582 A293134 A293053 * A163972 A068464 A244679 Adjacent sequences:  A144105 A144106 A144107 * A144109 A144110 A144111 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Sep 11 2008 EXTENSIONS Typo in row for n=7 corrected by Olivier Gérard, Oct 30 2012 STATUS approved

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Last modified October 22 18:55 EDT 2018. Contains 316500 sequences. (Running on oeis4.)