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 A085771 Triangle A059438(n,k), 0<=k<=n, with an extra column of zeros. 5
 1, 0, 1, 0, 1, 1, 0, 3, 2, 1, 0, 13, 7, 3, 1, 0, 71, 32, 12, 4, 1, 0, 461, 177, 58, 18, 5, 1, 0, 3447, 1142, 327, 92, 25, 6, 1, 0, 29093, 8411, 2109, 531, 135, 33, 7, 1, 0, 273343, 69692, 15366, 3440, 800, 188, 42, 8, 1, 0, 2829325, 642581, 125316, 24892, 5226, 1146, 252, 52, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 262 (#14). LINKS FindStat - Combinatorial Statistic Finder, The decomposition number of a permutation. FORMULA Let f(x) = Sum_{n>=0} n!*x^n, g(x) = 1 - 1/f(x). Then g(x) is g.f. for second diagonal A003319. Triangle T(n, k) read by rows, given by [0, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, ...] DELTA A000007 where DELTA is Deléham's operator defined in A084938. G.f.: 1/(1-xy/(1-x/(1-2x/(1-2x/(1-3x/(1-3x/(1-4x/(1-.... (continued fraction). [Paul Barry, Jan 29 2009] EXAMPLE Triangle starts:   1;   0,  1;   0,  1, 1;   0,  3, 2, 1;   0, 13, 7, 3, 1;   ... CROSSREFS Cf. A003319, A059439, A059440, A055998, A059438. Cf. A000007, A084938. T(2n,n) gives A308650. Sequence in context: A259790 A246654 A325111 * A253286 A284799 A111106 Adjacent sequences:  A085768 A085769 A085770 * A085772 A085773 A085774 KEYWORD easy,nonn,tabl AUTHOR Philippe Deléham, Jul 22 2003 STATUS approved

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Last modified April 15 10:22 EDT 2021. Contains 342977 sequences. (Running on oeis4.)