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A327032
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a(n) = T(n, 4) with T(n, k) = Sum_{d|k} phi(d)*binomial(n - 1 + k/d, k/d).
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1
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0, 4, 12, 27, 53, 95, 159, 252, 382, 558, 790, 1089, 1467, 1937, 2513, 3210, 4044, 5032, 6192, 7543, 9105, 10899, 12947, 15272, 17898, 20850, 24154, 27837, 31927, 36453, 41445, 46934, 52952, 59532, 66708, 74515, 82989, 92167, 102087, 112788, 124310, 136694
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: ((2*x^2 - 3*x + 2)*(x - 2)*x)/(x - 1)^5.
a(n) = ((7*n^2 - 14*n - 9)*a(n-1) - 2*(2*n^2 + n - 3)*a(n-2))/(3*(n^2 - 4*n + 3)) for n >= 4.
a(n) = n*(n*(n*(n + 6) + 23) + 66)/24.
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MAPLE
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a := n -> n*(n*(n*(n + 6) + 23) + 66)/24:
seq(a(n), n=0..41);
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MATHEMATICA
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Table[(66n+23n^2+6n^3+n^4)/24, {n, 0, 50}] (* Harvey P. Dale, Mar 10 2020 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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