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A146531
Triangle read by rows: a(n) = 3^floor(n/2)*Gamma(1 + floor(n/2)); t(n,m) = a(n)/(a(n - m)*a(m)).
1
1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 6, 2, 6, 1, 1, 1, 2, 2, 1, 1, 1, 9, 3, 18, 3, 9, 1, 1, 1, 3, 3, 3, 3, 1, 1, 1, 12, 4, 36, 6, 36, 4, 12, 1, 1, 1, 4, 4, 6, 6, 4, 4, 1, 1, 1, 15, 5, 60, 10, 90, 10, 60, 5, 15, 1
OFFSET
0,5
COMMENTS
The row sums are: {1, 2, 5, 4, 16, 8, 44, 16, 112, 32, 272}.
The matrix inverse starts
1;
-1,1;
2,-3,1;
-2,2,-1,1;
13,-12,4,-6,1;
-13,13,-4,4,-1,1;
116,-117,39,-36,6,-9,1;
-116,116,-39,39,-6,6,-1,1;
1393,-1392,464,-468,78,-72,8,-12,1;
-1393,1393,-464,464,-78,78,-8,8,-1,1;
- R. J. Mathar, Apr 08 2013
FORMULA
t(n,m) = a(n)/( a(n-m)*a(m) ), where a(n) = A032031(floor(n/2)).
EXAMPLE
1;
1, 1;
1, 3, 1;
1, 1, 1, 1;
1, 6, 2, 6, 1;
1, 1, 2, 2, 1, 1;
1, 9, 3, 18, 3, 9, 1;
1, 1, 3, 3, 3, 3, 1, 1;
1, 12, 4, 36, 6, 36, 4, 12, 1;
1, 1, 4, 4, 6, 6, 4, 4, 1, 1;
1, 15, 5, 60, 10, 90, 10, 60, 5, 15,1;
MAPLE
A032031 := proc(n)
3^n*n! ;
end proc:
A146531 := proc(n, m)
A032031(floor(n/2))/A032031(floor((n-m)/2))/A032031(floor(m/2)) ;
end proc: # R. J. Mathar, Apr 08 2013
MATHEMATICA
Clear[a, n, t]; a[n_] = 3^Floor[n/2]*Gamma[1 + Floor[n/2]]; t[n_, m_] = a[n]/(a[n - m]*a[m]); Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
CROSSREFS
Sequence in context: A143261 A204116 A093421 * A285865 A360098 A318451
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Oct 30 2008
STATUS
approved