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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 Table of n, a(n) for n=1..20. 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). Cf. A062024, A302583. Cf. A000169, A007778, A092364, A081131. Sequence in context: A043024 A144889 A176097 * A173429 A172134 A098916 Adjacent sequences: A345630 A345631 A345632 * A345634 A345635 A345636 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.)