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 A116963 Inverse Moebius transform of the shifted tetrahedral numbers. 10
 4, 14, 24, 49, 60, 118, 124, 214, 244, 356, 368, 608, 564, 814, 896, 1183, 1144, 1668, 1544, 2162, 2168, 2678, 2604, 3698, 3336, 4228, 4304, 5344, 4964, 6732, 5988, 7728, 7528, 8924, 8616, 11297, 9884, 12214, 12064, 14668, 13248, 17132, 15184, 18928, 18412, 21038 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 FORMULA a(n) = Sum_{d|n} (d+1)*(d+2)*(d+3)/6 = Sum_{d|n} A000292(d+1). G.f.: Sum_{k>0} (1/(1-x^k)^4 - 1). - Seiichi Manyama, Jun 12 2023 EXAMPLE a(12) = ((1+1)*(1+2)*(1+3)/6) + ((2+1)*(2+2)*(2+3)/6) + ((3+1)*(3+2)*(3+3)/6) + ((4+1)*(4+2)*(4+3)/6) + ((6+1)*(6+2)*(6+3)/6) + ((12+1)*(12+2)*(12+3)/6) = 4 + 10 + 20 + 35 + 84 + 455 = 608. a(13) = ((1+1)*(1+2)*(1+3)/6) + ((13+1)*(13+2)*(13+3)/6) = 4 + 560 = 564. MATHEMATICA a[n_] := DivisorSum[n, Binomial[# + 3, 3] &]; Array[a, 50] (* Amiram Eldar, Jul 05 2023 *) PROG (PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, 1/(1-x^k)^4-1)) \\ Seiichi Manyama, Jun 12 2023 CROSSREFS See also: A007437 (inverse Moebius transform of triangular numbers). Cf. A000292, A007437, A007503. Cf. A059358, A363604, A363607, A363611. Sequence in context: A277591 A017317 A195973 * A094930 A289665 A080286 Adjacent sequences: A116960 A116961 A116962 * A116964 A116965 A116966 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Mar 31 2006 STATUS approved

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Last modified May 21 07:02 EDT 2024. Contains 372729 sequences. (Running on oeis4.)