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A294603 Number of words of semilength n over n-ary alphabet, either empty or beginning with the first letter of the alphabet, such that the index set of occurring letters is an integer interval [1, k], that can be built by repeatedly inserting doublets into the initially empty word. 3
1, 1, 3, 20, 231, 3864, 85360, 2353546, 77963599, 3019479344, 133966276692, 6702399275538, 373406941221160, 22930441709648290, 1539004344848618466, 112089683771614695478, 8805334896381292460191, 742162775145283382779168, 66809386370870410069346476 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..350

FORMULA

a(n) = Sum_{k=0..n} A256116(n,k).

EXAMPLE

a(0) = 1: the empty word.

a(1) = 1: aa.

a(2) = 3: aaaa, aabb, abba.

a(3) = 20: aaaaaa, aaaabb, aaabba, aabaab, aabbaa, aabbbb, aabbcc, aabccb, aacbbc, aaccbb, abaaba, abbaaa, abbabb, abbacc, abbbba, abbcca, abccba, acbbca, accabb, accbba.

MAPLE

A:= proc(n, k) option remember; `if`(n=0, 1, k/n*

      add(binomial(2*n, j) *(n-j) *(k-1)^j, j=0..n-1))

    end:

T:= proc(n, k) option remember;

      add(A(n, k-i)*(-1)^i*binomial(k, i), i=0..k)/`if`(k=0, 1, k)

    end:

a:= n-> add(T(n, k), k=0..n):

seq(a(n), n=0..20);

CROSSREFS

Row sums of A256116.

Cf. A258498.

Sequence in context: A119758 A108527 A194972 * A240957 A335871 A195135

Adjacent sequences:  A294600 A294601 A294602 * A294604 A294605 A294606

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 03 2017

STATUS

approved

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Last modified August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)