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A261894 Number of compositions of n where the (possibly scattered) maximal subsequence of part i with multiplicity j is marked with a word of length j over an a(i-1)-ary alphabet whose letters appear in alphabetical order. 2
1, 1, 2, 5, 14, 42, 131, 425, 1405, 4768, 16355, 57112, 200908, 715945, 2563950, 9275069, 33670472, 123183827, 451968108, 1668602686, 6173397451, 22959862085, 85535398344, 320037864300, 1199162682255, 4509735549128, 16979368985245, 64134400212097 (list; graph; refs; listen; history; text; internal format)



Alois P. Heinz, Table of n, a(n) for n = 0..1000


a(4) = 14: 4a, 4b, 4c, 4d, 4e, 3a1a, 3b1a, 1a3a, 1a3b, 22aa 2a11aa, 12a1aa, 11aa2a, 1111aaaa.

a(5) = 42: 5a, 5b, 5c, 5d, 5e, 5f, 5g, 5h, 5i, 5j, 5k, 5l, 5m, 5n, 4a1a, 4b1a, 4c1a, 4d1a, 4e1a, 1a4a, 1a4b, 1a4c, 1a4d, 1a4e, 3a2a, 3b2a, 2a3a, 2a3b, 3a11aa, 3b11aa, 13a1aa, 13b1aa, 11aa3a, 11aa3b, 22aa1a, 21a2aa, 1a22aa, 2a111aaa, 12a11aaa, 112a1aaa, 111aaa2a, 11111aaaaa.

a(6) = 131: 6a, ..., 33aa, 33ab, 33bb, ..., 111111aaaaaa. The marked composition 33ba is not in this list.


b:= proc(n, i, p) option remember; `if`(n=0, p!,

      `if`(i<1, 0, add((t-> binomial(t+j-1, t-1))(

       a(i-1))*b(n-i*j, i-1, p+j)/j!, j=0..n/i)))


a:= n-> b(n$2, 0):

seq(a(n), n=0..30);


Cf. A000108 (without order restriction), A032009 (with distinct parts).

Sequence in context: A261588 A006930 A036767 * A287969 A061922 A293498

Adjacent sequences:  A261891 A261892 A261893 * A261895 A261896 A261897




Alois P. Heinz, Sep 05 2015



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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)