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A319576
a(n) = (4/15)*n*(n - 1)*(n^3 - 9*n^2 + 26*n - 9).
4
0, 0, 8, 24, 48, 112, 312, 840, 2016, 4320, 8424, 15224, 25872, 41808, 64792, 96936, 140736, 199104, 275400, 373464, 497648, 652848, 844536, 1078792, 1362336, 1702560, 2107560, 2586168, 3147984, 3803408, 4563672, 5440872, 6448000, 7598976, 8908680, 10392984
OFFSET
0,3
FORMULA
a(n) = [x^5] JacobiTheta3(x)^n.
a(n) = A319574(n,5).
From Colin Barker, Oct 02 2018: (Start)
G.f.: 8*x^2*(1 - 3*x + 3*x^2 + 3*x^3) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>5.
(End)
MAPLE
a := n -> (4/15)*n*(n - 1)*(n^3 - 9*n^2 + 26*n - 9):
seq(a(n), n=0..41);
MATHEMATICA
A319576[n_] := 4/15*n*(n-1)*(n^3-9*n^2+26*n-9); Array[A319576, 50, 0] (* or *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 0, 8, 24, 48, 112}, 50] (* Paolo Xausa, Feb 20 2024 *)
PROG
(PARI) concat([0, 0], Vec(8*x^2*(1 - 3*x + 3*x^2 + 3*x^3) / (1 - x)^6 + O(x^40))) \\ Colin Barker, Oct 02 2018
CROSSREFS
Cf. A000012 (m=0), A005843 (m=1), A046092 (m=2), A130809 (m=3), A319575 (m=4), this sequence (m=5), A319577 (m=6).
Column n=5 of A122141.
Cf. A319574.
Sequence in context: A333714 A146980 A342062 * A028612 A333173 A358036
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Oct 01 2018
STATUS
approved