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

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..425

Formula

E.g.f.: Sum_{i>=0} x^i/(i! * (1 - Sum_{j=1..i} x^j/j!)).

Example

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).

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

Prog

(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!))))))}

Crossrefs

Cf. A000262, A000670, A006153, A308876.

Sequence in context: A249479 A355154 A236410 * A339836 A385544 A105748

Adjacent sequences: A386371 A386372 A386373 * A386375 A386376 A386377

Keyword

nonn,easy

Author

John Tyler Rascoe, Jul 19 2025

Status

approved