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A261744 Number of partitions of n where each part i is marked with a word of length i over a denary alphabet whose letters appear in alphabetical order. 2
1, 10, 155, 1770, 21440, 228502, 2544125, 26385600, 279082750, 2855995900, 29442232007, 298239664140, 3034263224145, 30563607210830, 308545853368510, 3098369166354518, 31146484546140435, 312188428888116430, 3131008962348253370, 31350509429122574890 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) ~ c * 10^n, where c = Product_{k>=2} 1/(1 - binomial(k+9,9)/10^k) = 3.1513858636401513585013047835048959202713435... - Vaclav Kotesovec, Oct 11 2017, updated May 10 2021
G.f.: Product_{k>=1} 1 / (1 - binomial(k+9,9)*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+9, 9))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..30);
CROSSREFS
Column k=10 of A261718.
Sequence in context: A061654 A298081 A240374 * A229284 A087603 A292837
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 30 2015
STATUS
approved

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Last modified July 13 01:42 EDT 2024. Contains 374259 sequences. (Running on oeis4.)