# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a094953
Showing 1-1 of 1

%I A094953 #9 Dec 03 2018 05:06:32
%S A094953 1,1,2,2,4,3,2,8,9,4,3,12,21,16,5,3,18,39,44,25,6,4,24,66,96,80,36,7,
%T A094953 4,32,102,184,200,132,49,8,5,40,150,320,430,372,203,64,9,5,50,210,520,
%U A094953 830,888,637,296,81,10,6,60,285,800,1480,1884,1673,1024,414,100,11,6
%N A094953 Triangle T(n,m) read by rows: number of rises (drops) in the compositions of n with m parts, m>=2.
%H A094953 S. Heubach and T. Mansour, <a href="https://arxiv.org/abs/math/0310197">Counting rises, levels and drops in compositions</a>, arXiv:math/0310197 [math.CO], 2003.
%F A094953 G.f. of m-th column: [(m-1)x^(m+1)]/[(1+x)(1-x)^m].
%e A094953 1
%e A094953 1 2
%e A094953 2 4 3
%e A094953 2 8 9 4
%e A094953 3 12 21 16 5
%e A094953 3 18 39 44 25 6
%e A094953 4 24 66 96 80 36 7
%t A094953 T[n_, m_] := SeriesCoefficient[(m-1)x^(m+1)/(1+x)/(1-x)^m, {x, 0, n+1}];
%t A094953 Table[T[n, m], {n, 2, 13}, {m, 2, n}] // Flatten (* _Jean-François Alcover_, Dec 03 2018 *)
%o A094953 (PARI) T(n,m)=polcoeff((m-1)*x^(m+1)/(1+x)/(1-x)^m,n)
%Y A094953 Columns 2-4 (+-offset) are A004526, A007590, A007518.
%Y A094953 Row sums are A045883, diagonals include n, n^2, (n-1)(n^2-n+2)/2, (n-1)^2(n^+n+6), etc.
%Y A094953 Cf. A045927.
%K A094953 nonn,tabl
%O A094953 2,3
%A A094953 _Ralf Stephan_, May 26 2004

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE