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A261741 Number of partitions of n where each part i is marked with a word of length i over a septenary alphabet whose letters appear in alphabetical order. 2
1, 7, 77, 623, 5355, 40299, 317905, 2323483, 17353028, 124991685, 907465307, 6458846989, 46199021001, 326573565143, 2314422214435, 16296707707077, 114891467946017, 806991845455033, 5672334432498356, 39785054428093380, 279156880971492454, 1956352659297436368 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) ~ c * 7^n, where c = Product_{k>=2} 1/(1 - binomial(k+6,6)/7^k) = 3.519268129363442517546929108933080435102442778133731795486515352... - Vaclav Kotesovec, Oct 11 2017, updated May 10 2021
G.f.: Product_{k>=1} 1 / (1 - binomial(k+6,6)*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+6, 6))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..30);
CROSSREFS
Column k=7 of A261718.
Sequence in context: A213261 A268958 A068667 * A228414 A043042 A191465
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 30 2015
STATUS
approved

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Last modified June 12 17:26 EDT 2024. Contains 373349 sequences. (Running on oeis4.)