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

0,3

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

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

Crossrefs

Column k=10 of A293108.

Cf. A212916, A293110, A293749.

Sequence in context: A293737 A293738 A293739 * A293110 A322204 A000227

Adjacent sequences: A293737 A293738 A293739 * A293741 A293742 A293743

Keyword

nonn

Author

Alois P. Heinz, Oct 15 2017

Status

approved