A386374 Number of words of length n over an infinite alphabet such that the letters cover an initial interval and the letter 1 occurs at least as many times as any other letter.
1, 1, 3, 10, 47, 276, 2022, 17606, 179391, 2093860, 27581888, 404680398, 6541528886, 115437202986, 2206844818622, 45408726154590, 1000134868827263, 23468606700087972, 584340284516996400, 15383829737201853518, 426915367401366308112, 12454073547413511363878
Offset: 0
Examples
a(3) = 10 counts: (1,1,1), (1,1,2), (1,2,1), (1,2,3), (1,3,2), (2,1,1), (2,1,3), (2,3,1), (3,1,2), (3,2,1).
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..425
Programs
-
Maple
b:= proc(n, t) option remember; `if`(n=0, 1, add(b(n-j, t)/j!, j=1..min(n, t))) end: a:= n-> n!*add(b(n-j, j)/j!, j=0..n): seq(a(n), n=0..21); # Alois P. Heinz, Jul 19 2025 -
PARI
A_x(N) = {my(x='x+O('x^N)); Vec(serlaplace(sum(i=0,N, x^i/(i! *(1-sum(j=1,i, x^j/j!))))))}
Formula
E.g.f.: Sum_{i>=0} x^i/(i! * (1 - Sum_{j=1..i} x^j/j!)).