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A261740 Number of partitions of n where each part i is marked with a word of length i over a senary alphabet whose letters appear in alphabetical order. 2
1, 6, 57, 398, 2955, 19158, 130453, 820554, 5280204, 32711022, 204324819, 1249546656, 7682267669, 46625705988, 283766862009, 1714704081724, 10374896682273, 62511439251768, 376943252871343, 2267304042230202, 13643684237963994, 81983795625450144 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) ~ c * 6^n, where c = Product_{k>=2} 1/(1 - binomial(k+5,5)/6^k) = 3.760725122262068858184072984846959348360490081749654779894152320389687335... - Vaclav Kotesovec, Oct 11 2017, updated May 10 2021
G.f.: Product_{k>=1} 1 / (1 - binomial(k+5,5)*x^k). - Ilya Gutkovskiy, May 09 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+5, 5))))
end:
a:= n-> b(n$2):
seq(a(n), n=0..30);
CROSSREFS
Column k=6 of A261718.
Sequence in context: A227813 A221575 A001593 * A296027 A229280 A124546
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 30 2015
STATUS
approved

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Last modified June 12 10:55 EDT 2024. Contains 373331 sequences. (Running on oeis4.)