The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A360794 Expansion of Sum_{k>0} x^k / (1 - k * x^k)^(k+1). 3
 1, 3, 4, 11, 6, 43, 8, 109, 100, 281, 12, 1507, 14, 1863, 3376, 6937, 18, 26245, 20, 53211, 63022, 67739, 24, 572413, 78776, 372945, 1087048, 1761719, 30, 7362871, 32, 9947953, 16897486, 10027349, 8011116, 123101515, 38, 49807779, 241823440, 361722421, 42 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..41. FORMULA a(n) = Sum_{d|n} d^(n/d-1) * binomial(d+n/d-1,d). If p is prime, a(p) = 1 + p. MATHEMATICA a[n_] := DivisorSum[n, #^(n/# - 1) * Binomial[# + n/# - 1, #] &]; Array[a, 40] (* Amiram Eldar, Jul 31 2023 *) PROG (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-k*x^k)^(k+1))) (PARI) a(n) = sumdiv(n, d, d^(n/d-1)*binomial(d+n/d-1, d)); CROSSREFS Cf. A360782, A360783. Cf. A081543, A324158. Sequence in context: A360948 A175317 A056045 * A220848 A232891 A096223 Adjacent sequences: A360791 A360792 A360793 * A360795 A360796 A360797 KEYWORD nonn AUTHOR Seiichi Manyama, Feb 21 2023 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 28 04:05 EST 2023. Contains 367394 sequences. (Running on oeis4.)