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A351732
Number of length n word structures using an infinite alphabet with all distinct run-lengths and the first run length of a symbol less than that of previous symbols.
2
1, 1, 1, 2, 2, 3, 7, 8, 12, 17, 46, 51, 84, 114, 172, 437, 520, 810, 1153, 1699, 2298, 6075, 6955, 11219, 15561, 23308, 31133, 45544, 107379, 128475, 200201, 281480, 413389, 561028, 806643, 1071165, 2514418, 2952086, 4619012, 6364285, 9436458
OFFSET
0,4
COMMENTS
Permuting the symbols does not change the structure.
LINKS
EXAMPLE
The a(3) = 2 word structures are 111, 112.
The a(4) = 2 word structures are 1111, 1112.
The a(5) = 3 word structures are 11111, 11112, 11122.
The a(6) = 7 word structures are 111111, 111112, 111122, 111221, 111211, 112111, 111223.
PROG
(PARI)
P(n) = {Vec(-1 + prod(k=1, n, 1 + y*x^k + O(x*x^n)))}
R(u, k) = {k*[subst(serlaplace(p)/y, y, k-1) | p<-u]}
seq(n)={my(u=P(n)); concat([1], sum(k=1, n, R(u, k)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)/(r!)^2) ))}
CROSSREFS
Row sums of A351645.
Cf. A351638.
Sequence in context: A259254 A095017 A141559 * A211395 A160433 A043550
KEYWORD
nonn
AUTHOR
Andrew Howroyd, May 20 2022
STATUS
approved