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A158193
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Irregular triangle T(n, k) = ((-1)^(k+1)/2)*Sum_{j=0..n-2*k} binomial(n+2, j)*binomial(n+2, j+k+1)* binomial(n+2, j+2*k+2), read by rows.
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1
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-1, -9, -72, 3, -550, 50, -4140, 585, -10, -31017, 5880, -245, -232288, 54488, -3808, 35, -1742148, 480816, -47880, 1134, -13095450, 4110750, -532350, 22050, -126, -98687600, 34397880, -5466780, 333960, -5082, -745652160, 283510260, -53143200, 4348377, -118800, 462
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listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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FORMULA
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T(n, k) = ((-1)^(k+1)/2)*Sum_{j=0..n-2*k} binomial(n+2, j)*binomial(n+2, j+k+1)* binomial(n+2, j+2*k+2).
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EXAMPLE
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Irregular triangle begins as:
-1;
-9;
-72, 3;
-550, 50;
-4140, 585, -10;
-31017, 5880, -245;
-232288, 54488, -3808, 35;
-1742148, 480816, -47880, 1134;
-13095450, 4110750, -532350, 22050, -126;
-98687600, 34397880, -5466780, 333960, -5082;
-745652160, 283510260, -53143200, 4348377, -118800, 462;
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MATHEMATICA
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Table[Sum[(-1)^(k+1)*Binomial[n+2, j]*Binomial[n+2, j+k+1]*Binomial[n+2, j+2*k+2], {j, 0, n-2*k}]/2, {n, 0, 10}, {k, 0, Floor[n/2]}]//Flatten
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PROG
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(Magma)
A158193:= func< n, k | ((-1)^(k+1)/2)*(&+[Binomial(n+2, j)*Binomial(n+2, j+k+1)*Binomial(n+2, j+2*k+2): j in [0..n-2*k]]) >;
(Sage)
def A158193(n, k): return ((-1)^(k+1)/2)*sum( binomial(n+2, j)*binomial(n+2, j+k+1)*binomial(n+2, j+2*k+2) for j in (0..n-2*k) )
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CROSSREFS
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KEYWORD
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sign,tabf
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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