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1, -1, 2, 1, -2, 3, -1, 0, 0, 4, 1, 4, -12, 8, 5, -1, -10, 30, -40, 25, 6, 1, 18, -45, 60, -75, 54, 7, -1, -28, 42, 0, 0, -84, 98, 8, 1, 40, 0, -224, 420, -336, 0, 160, 9, -1, -54, -108, 672, -1260, 1512, -1176, 288, 243, 10
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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Row sums = A001405: (1, 1, 2, 3, 6, 10, 10, ...).
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LINKS
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FORMULA
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Inverse binomial transform of A132814.
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EXAMPLE
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First few rows of the triangle:
1;
-1, 2;
1, -2, 3;
-1, 0, 0, 4;
1, 4, -12, 8, 5;
-1, -10, 30, -240, 25, 6;
1, 18, -45, 60, -75, 54, 7;
...
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PROG
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(PARI) tabl(nn) = {t007318 = matrix(nn, nn, n, k, binomial(n-1, k-1)); t132813 = matrix(nn, nn, n, k, binomial(n-1, k-1)*binomial(n, k-1)); t132814 = t007318^(-1)*t132813; t132815 = t007318^(-1)*t132814; for (n=1, nn, for (k=1, n, print1(t132815[n, k], ", "); ); ); } \\ Michel Marcus, Feb 12 2014
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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