

A094953


Triangle T(n,m) read by rows: number of rises (drops) in the compositions of n with m parts, m>=2.


4



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, 4, 32, 102, 184, 200, 132, 49, 8, 5, 40, 150, 320, 430, 372, 203, 64, 9, 5, 50, 210, 520, 830, 888, 637, 296, 81, 10, 6, 60, 285, 800, 1480, 1884, 1673, 1024, 414, 100, 11, 6
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OFFSET

2,3


LINKS

Table of n, a(n) for n=2..68.
S. Heubach and T. Mansour, Counting rises, levels and drops in compositions


FORMULA

G.f. of mth column: [(m1)x^(m+1)]/[(1+x)(1x)^m].


EXAMPLE

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


PROG

(PARI) T(n, m)=polcoeff((m1)*x^(m+1)/(1+x)/(1x)^m, n)


CROSSREFS

Columns 24 (+offset) are A004526, A007590, A007518.
Row sums are A045883, diagonals include n, n^2, (n1)(n^2n+2)/2, (n1)^2(n^+n+6), etc.
Cf. A045927.
Sequence in context: A112154 A112155 A209749 * A122687 A002948 A117113
Adjacent sequences: A094950 A094951 A094952 * A094954 A094955 A094956


KEYWORD

nonn,tabl


AUTHOR

Ralf Stephan, May 26 2004


STATUS

approved



