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A261799
Number of 7-compositions of n: matrices with 7 rows of nonnegative integers with positive column sums and total element sum n.
2
1, 7, 77, 819, 8687, 92141, 977347, 10366833, 109962202, 1166381804, 12371946734, 131230670312, 1391978902090, 14764881252772, 156612803600094, 1661210126351328, 17620647995924820, 186904251828901124, 1982515022137687464, 21028766197355391048
OFFSET
0,2
COMMENTS
Also the number of compositions of n where each part i is marked with a word of length i over a septenary alphabet whose letters appear in alphabetical order.
FORMULA
G.f.: (1-x)^7/(2*(1-x)^7-1).
a(n) = A261780(n,7).
a(n) = Sum_{k>=0} (1/2)^(k+1) * binomial(n-1+7*k,n). - Seiichi Manyama, Aug 06 2024
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*binomial(j+6, 6), j=1..n))
end:
seq(a(n), n=0..20);
CROSSREFS
Column k=7 of A261780.
Sequence in context: A061546 A002281 A097983 * A246236 A349364 A267709
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 01 2015
STATUS
approved