A327032 a(n) = T(n, 4) with T(n, k) = Sum_{d|k} phi(d)*binomial(n - 1 + k/d, k/d).

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

Author

Peter Luschny, Aug 25 2019

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A327031 (square array), A000004 (k=0), A001477 (k=1), A000096 (k=2), A255993 (k=3 conj.), this sequence (k=4).

Programs

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 *)

PARI

a(n)=n*(n*(n*(n+6)+23)+66)/24 \\ Charles R Greathouse IV, Oct 21 2022

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.