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%I #14 Apr 19 2021 07:09:39
%S 1,7,22,63,127,280,463,855,1309,2135,3004,4704,6189,9037,11776,16359,
%T 20350,27901,33650,44695,53614,68790,80731,103776,118882,148701,
%U 171220,210469,237337,292292,324633,393351,438922,522298,576346,690333,749399
%N Inverse Moebius transform of 5-simplex numbers A000389.
%H Seiichi Manyama, <a href="/A101289/b101289.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Sum_{d|n} d*(d+1)*(d+2)*(d+3)*(d+4)/120. a(n) = Sum_{d|n} C(d+4,5). a(n) = Sum{d|n} A000389(d). a(n) = Sum_{d|n} (d^5-10*d^4+35*d^3-50*d^2+24*d)/120.
%F G.f.: Sum_{k>=1} x^k/(1 - x^k)^6 = Sum_{k>=1} binomial(k+4,5) * x^k/(1 - x^k). - _Seiichi Manyama_, Apr 19 2021
%o (PARI) a(n) = sumdiv(n, d, binomial(d+4, 5)); \\ _Seiichi Manyama_, Apr 19 2021
%o (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, binomial(k+4, 5)*x^k/(1-x^k))) \\ _Seiichi Manyama_, Apr 19 2021
%Y See also: A007437 = inverse Moebius transform of triangular numbers, A116963 = inverse Moebius transform of tetrahedral numbers. Cf. A073570.
%Y Cf. A000389, A007437, A116963, A332508.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Mar 31 2006
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