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A131087
Triangle read by rows: T(n,k) = 2*binomial(n,k) - (1 + (-1)^(n-k))/2 (0 <= k <= n).
1
1, 2, 1, 1, 4, 1, 2, 5, 6, 1, 1, 8, 11, 8, 1, 2, 9, 20, 19, 10, 1, 1, 12, 29, 40, 29, 12, 1, 2, 13, 42, 69, 70, 41, 14, 1, 1, 16, 55, 112, 139, 112, 55, 16, 1, 2, 17, 72, 167, 252, 251, 168, 71, 18, 1, 1, 20, 89, 240, 419, 504, 419, 240, 89, 20, 1, 2, 21, 110, 329, 660, 923, 924
OFFSET
0,2
COMMENTS
Row sums = A084174: (1, 3, 6, 14, 29, ...).
2*A007318 - A128174 as infinite lower triangular matrices. - Emeric Deutsch, Jun 21 2007
FORMULA
G.f.: G(t,z) = (1 + z - tz - 2z^2 + 2tz^3)/((1-z^2)*(1-tz)*(1-z-tz)). - Emeric Deutsch, Jun 21 2007
EXAMPLE
First few rows of the triangle:
1;
2, 1;
1, 4, 1;
2, 5, 6, 1;
1, 8, 11, 8, 1;
2, 9, 20, 19, 10, 1;
1, 12, 29, 40, 29, 12, 1;
...
MAPLE
T := proc (n, k) options operator, arrow; 2*binomial(n, k)-1/2-(1/2)*(-1)^(n-k) end proc; for n from 0 to 11 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jun 21 2007
CROSSREFS
Sequence in context: A193554 A372701 A131350 * A105475 A249061 A334178
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 14 2007
EXTENSIONS
More terms from Emeric Deutsch, Jun 21 2007
STATUS
approved