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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. 2
1, 8, 100, 920, 8986, 77000, 690652, 5752280, 48916087, 401709720, 3324377084, 26996501992, 220265771738, 1777445952616, 14377907329724, 115613187110872, 930725344479074, 7467529999843432, 59954521406306500, 480433200037686456, 3851244156978563566 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 30 2015
STATUS
approved

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Last modified July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)