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A345633 Sum of terms of odd index in the binomial decomposition of n^(n-1). 1
0, 1, 4, 36, 272, 4400, 51012, 1188544, 18640960, 567108864, 11225320100, 421504185344, 10079828372880, 450353989316608, 12627774819845668, 654244800082329600, 21046391759976988928, 1240529732459024678912, 45032132922921758270916, 2975557672677668838178816 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
When writing n^(n-1) (A000169) as a sum of powers of n using the binomial theorem, one can separately sum the even and the odd powers of n. This is the odd part. See the Formula section.
LINKS
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.
MATHEMATICA
Table[Plus @@ Table[(n - 1)^(2 k + 1) Binomial[n - 1, 2 k + 1], {k, 0, Floor[(n - 1)/2]}], {n, 1, 21}]
CROSSREFS
Cf. A345632 (even part).
Sequence in context: A043024 A144889 A176097 * A173429 A172134 A098916
KEYWORD
nonn,easy
AUTHOR
Olivier Gérard, Jun 21 2021
STATUS
approved

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Last modified April 17 04:44 EDT 2024. Contains 371756 sequences. (Running on oeis4.)