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Klee's Identity


Klee's identity is the binomial sum

 sum_(k=0)^n(-1)^k(n; k)(n+k; m)=(-1)^n(n; m-n),

where (n; k) is a binomial coefficient. For m=0, 1, ... and n=0, 1,..., the following array is obtained.

10000000000
0-1000000000
0-1100000000
002-10000000
001-31000000
000-34-100000
000-16-510000
00004-106-1000
00001-1015-7100
00000-520-218-10
00000-115-3528-91

(OEIS A092865)


See also

Binomial Sums

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References

Riordan, J. Combinatorial Identities. New York: Wiley, p. 13, 1979.Rota, G.-C.; Kahaner, D.; Odlyzko, A. "On the Foundations of Combinatorial Theory. VIII: Finite Operator Calculus." J. Math. Anal. Appl. 42, 684-760, 1973.Sloane, N. J. A. Sequence A092865 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Klee's Identity

Cite this as:

Weisstein, Eric W. "Klee's Identity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KleesIdentity.html

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