A345633 Sum of terms of odd index in the binomial decomposition of n^(n-1).
0, 1, 4, 36, 272, 4400, 51012, 1188544, 18640960, 567108864, 11225320100, 421504185344, 10079828372880, 450353989316608, 12627774819845668, 654244800082329600, 21046391759976988928, 1240529732459024678912, 45032132922921758270916, 2975557672677668838178816
Offset: 1
Programs
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Mathematica
Table[Plus @@ Table[(n - 1)^(2 k + 1) Binomial[n - 1, 2 k + 1], {k, 0, Floor[(n - 1)/2]}], {n, 1, 21}]
Formula
a(n+1) = Sum_{k=0..floor((n-1)/2)} n^(2k+1)*binomial(n, 2k+1).
a(n+1) = ((1 + n)^n - (1 - n)^n)/2.
Comments