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 A358411 a(n) = Sum_{d|n} (d + n/d - 1)!/(d - 1)!. 1
 1, 4, 9, 34, 125, 762, 5047, 40468, 362949, 3629560, 39916811, 479007174, 6227020813, 87178331590, 1307674370745, 20922790251808, 355687428096017, 6402373709377404, 121645100408832019, 2432902008216565330, 51090942171709621965, 1124000727778086681754 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..22. FORMULA G.f.: Sum_{k>0} k! * x^k/(1 - x^k)^(k+1). If p is prime, a(p) = p + p!. MATHEMATICA a[n_] := DivisorSum[n, (# + n/# - 1)!/(# - 1)! &]; Array[a, 22] (* Amiram Eldar, Aug 30 2023 *) PROG (PARI) a(n) = sumdiv(n, d, (d+n/d-1)!/(d-1)!); (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, k!*x^k/(1-x^k)^(k+1))) CROSSREFS Cf. A081543, A358389, A358410. Sequence in context: A149134 A149135 A149136 * A006392 A179079 A084449 Adjacent sequences: A358408 A358409 A358410 * A358412 A358413 A358414 KEYWORD nonn AUTHOR Seiichi Manyama, Nov 14 2022 STATUS approved

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Last modified July 13 17:35 EDT 2024. Contains 374284 sequences. (Running on oeis4.)