A261742 Number of partitions of n where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order.

1, 8, 100, 920, 8986, 77000, 690652, 5752280, 48916087, 401709720, 3324377084, 26996501992, 220265771738, 1777445952616, 14377907329724, 115613187110872, 930725344479074, 7467529999843432, 59954521406306500, 480433200037686456, 3851244156978563566

Offset

0,2

Links

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

Formula

a(n) ~ c * 8^n, where c = Product_{k>=2} 1/(1 - binomial(k+7,7)/8^k) = 3.3565128773700137140303140039343582841894554205106317247... - Vaclav Kotesovec, Oct 11 2017, updated May 10 2021

G.f.: Product_{k>=1} 1 / (1 - binomial(k+7,7)*x^k). - Ilya Gutkovskiy, May 10 2021

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      b(n, i-1)+`if`(i>n, 0, b(n-i, i)*binomial(i+7, 7))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..30);

Crossrefs

Column k=8 of A261718.

Sequence in context: A181034 A324067 A083227 * A222486 A229282 A179485

Adjacent sequences: A261739 A261740 A261741 * A261743 A261744 A261745

Keyword

nonn

Author

Alois P. Heinz, Aug 30 2015

Status

approved