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A133601
A007318 * (A097806 + A133080 - I), I = Identity matrix.
1
1, 3, 1, 5, 3, 1, 7, 6, 5, 1, 9, 10, 14, 5, 1, 11, 15, 30, 15, 7, 1, 13, 21, 55, 35, 27, 7, 1, 15, 28, 91, 70, 77, 28, 9, 1, 17, 36, 140, 126, 182, 84, 44, 9, 1, 19, 45, 204, 210, 378, 210, 156, 45, 11, 1
OFFSET
0,2
FORMULA
A007318 * (A097806 + A133080 - I), I = Identity matrix. Binomial transform of an infinite lower triangular matrix with (1,1,1,...) in the main diagonal and (2,1,2,1,2,...) in the subdiagonal; and the rest zeros.
EXAMPLE
First few rows of the triangle are:
1;
3, 1;
5, 3, 1;
7, 6, 5, 1;
9, 10, 14, 5, 1;
11, 15, 30, 15, 7, 1;
13, 21, 55, 35, 27, 7, 1;
15, 28, 91, 70, 77, 28, 9, 1;
...
MAPLE
A133601aux := proc(n, k)
if n <> k then
A097806(n, k)+A133080(n, k) ;
else
A097806(n, k)+A133080(n, k)-1 ;
end if;
end proc:
A133601 := proc(n, k)
add( A007318(n, j)*A133601aux(j+1, k+1), j=k..n) ;
end proc: # R. J. Mathar, Jun 20 2015
CROSSREFS
Cf. A097806, A133080, A052549 (row sums).
Sequence in context: A099375 A348835 A130301 * A258207 A133094 A300437
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Sep 18 2007
STATUS
approved