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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 (list; graph; refs; listen; history; text; internal format)
 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 Alois P. Heinz, Table of n, a(n) for n = 0..850 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 Adjacent sequences: A261799 A261800 A261801 * A261803 A261804 A261805 KEYWORD nonn,easy AUTHOR Alois P. Heinz, Sep 01 2015 STATUS approved

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Last modified September 8 22:39 EDT 2024. Contains 375759 sequences. (Running on oeis4.)