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%I #17 Nov 06 2017 02:43:37
%S 1,1,2,1,6,4,1,14,22,8,1,30,86,64,16,1,62,294,346,168,32,1,126,938,
%T 1594,1140,416,64,1,254,2874,6746,6422,3376,992,128,1,510,8586,27098,
%U 32758,22192,9344,2304,256,1,1022,25234,105090,157326,129914,69840,24672,5248,512
%N Regular triangle array: number of [0-r]-covering hierarchies with thickness = e.
%H G. Kreweras, <a href="http://www.numdam.org/item?id=BURO_1973__20__3_0">Sur les hiérarchies de segments</a>, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, #20 (1973), p. 25-27.
%H G. Kreweras, <a href="/A001844/a001844.pdf">Sur les hiérarchies de segments</a>, Cahiers du Bureau Universitaire de Recherche Opérationnelle, Institut de Statistique, Université de Paris, #20 (1973). (Annotated scanned copy)
%F T(r, e) = A250484(r, e) - A250484(r-1, e).
%e Triangle starts:
%e 1;
%e 1, 2;
%e 1, 6, 4;
%e 1, 14, 22, 8;
%e 1, 30, 86, 64, 16;
%e 1, 62, 294, 346, 168, 32;
%e ...
%o (PARI) tabl(nn) = {v = vector(nn); v[1] = 1; for (n=2, nn, v[n] = 1 + t*v[n-1]^2/(1 - t*v[n-1]);); pv = vector(nn, n, v[n]+O(t^(nn+1))); m = matrix(nn, nn, n, k, polcoeff(pv[n], k-1, t)); m = m ~; for (n= 2, nn, for (k=2, n, print1(m[n, k]-m[n, k-1], ", ");); print(););}
%Y Cf. A000079 (right diagonal), A001003 (row sums), A250484.
%K nonn,tabl
%O 1,3
%A _Michel Marcus_, Nov 24 2014
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