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A106471
A number triangle with duplicated columns of the form 2^n - Sum_{j=0..2k-1} C(n,j).
1
1, 2, 1, 4, 2, 1, 8, 4, 4, 1, 16, 8, 11, 4, 1, 32, 16, 26, 11, 6, 1, 64, 32, 57, 26, 22, 6, 1, 128, 64, 120, 57, 64, 22, 8, 1, 256, 128, 247, 120, 163, 64, 37, 8, 1, 512, 256, 502, 247, 382, 163, 130, 37, 10, 1, 1024, 512, 1013, 502, 848, 382, 386, 130, 56, 10, 1, 2048, 1024
OFFSET
0,2
COMMENTS
Columns include A000079, A000295, A002663, A035038, A035040.
Row sums are A106472.
Product of binomial matrix binomial(n,k) and number triangle A106465.
FORMULA
Column 2k has g.f. x^(2*k)/((1-2*x)*(1-x)^(2*k-2)).
Column 2k+1 has g.f. x^(2*k+1)/((1-2*x)*(1-x)^(2*k)).
EXAMPLE
Triangle begins
1;
2, 1;
4, 2, 1;
8, 4, 4, 1;
16, 8, 11, 4, 1;
32, 16, 26, 11, 6, 1;
64, 32, 57, 26, 22, 6, 1;
CROSSREFS
Sequence in context: A235670 A130321 A101508 * A180870 A228565 A054453
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, May 03 2005
STATUS
approved