A293740 Number of multisets of nonempty words with a total of n letters over denary alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.

1, 1, 3, 7, 20, 54, 164, 500, 1630, 5472, 19257, 70132, 265845, 1042187, 4233556, 17747898, 76808746, 342105748, 1567582938, 7371055703, 35543320641, 175391546006, 884988267329, 4558168670317, 23945579145172, 128119583103268, 697657759802893, 3861749505389798

Offset: 0

Author

Alois P. Heinz, Oct 15 2017

Keywords

• nonn

Comments

This sequence differs from A293110 first at n=11.

In general, for k>2, is column k of A293108 asymptotic to c(k) * k^n / n^(k*(k-1)/4), where c(k) are constants dependent only on k. - Vaclav Kotesovec, Dec 19 2020

Links

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

Crossrefs

Column k=10 of A293108.

Cf. A212916, A293110, A293749.

Formula

G.f.: Product_{j>=1} 1/(1-x^j)^A212916(j).

a(n) ~ c * 10^n / n^(45/2), where c = 2738042932059662927432072.80048573... - Vaclav Kotesovec, Dec 19 2020