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Search: a327031 -id:a327031
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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).
+10
1
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
OFFSET
0,2
FORMULA
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.
MAPLE
a := n -> n*(n*(n*(n + 6) + 23) + 66)/24:
seq(a(n), n=0..41);
MATHEMATICA
Table[(66n+23n^2+6n^3+n^4)/24, {n, 0, 50}] (* Harvey P. Dale, Mar 10 2020 *)
PROG
(PARI) a(n)=n*(n*(n*(n+6)+23)+66)/24 \\ Charles R Greathouse IV, Oct 21 2022
CROSSREFS
Cf. A327031 (square array), A000004 (k=0), A001477 (k=1), A000096 (k=2), A255993 (k=3 conj.), this sequence (k=4).
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Aug 25 2019
STATUS
approved

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