04/10/23 23:46:09
>>814
留数計算とか知らんけど
Σ[k=0,n] k*C[2n,n-k]
=Σ[k=0,n] (n-k)*C[2n,k]
=nΣ[k=0,n]C[2n,k] - Σ[k=0,n] k*C[2n,k]
=nΣ[k=0,n]C[2n,k] - 2nΣ[k=1,n] C[2n-1,k-1]
=n(2^(2n)+C[2n,n])/2 - 2n(2^(2n-1))/2
=n/2C[2n,n]
でいいんじゃね？
04/10/23 23:46:09
>>814
留数計算とか知らんけど
Σ[k=0,n] k*C[2n,n-k]
=Σ[k=0,n] (n-k)*C[2n,k]
=nΣ[k=0,n]C[2n,k] - Σ[k=0,n] k*C[2n,k]
=nΣ[k=0,n]C[2n,k] - 2nΣ[k=1,n] C[2n-1,k-1]
=n(2^(2n)+C[2n,n])/2 - 2n(2^(2n-1))/2
=n/2C[2n,n]
でいいんじゃね？