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A261802
Number of 10-compositions of n: matrices with 10 rows of nonnegative integers with positive column sums and total element sum n.
2
1, 10, 155, 2320, 34640, 517252, 7723970, 115339960, 1722340115, 25719233330, 384058268507, 5735036957760, 85639736481880, 1278834734405320, 19096488909285540, 285162639746429024, 4258255614078447290, 63587365059302801520, 949532710487622388080
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 denary alphabet whose letters appear in alphabetical order.
LINKS
Index entries for linear recurrences with constant coefficients, signature (20, -90, 240, -420, 504, -420, 240, -90, 20, -2).
FORMULA
G.f.: (1-x)^10/(2*(1-x)^10-1).
a(n) = A261780(n,10).
a(n) = Sum_{k>=0} (1/2)^(k+1) * binomial(n-1+10*k,n). - Seiichi Manyama, Aug 06 2024
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*binomial(j+9, 9), j=1..n))
end:
seq(a(n), n=0..20);
CROSSREFS
Column k=10 of A261780.
Sequence in context: A229284 A087603 A292837 * A246239 A235340 A306034
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Sep 01 2015
STATUS
approved