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A319577
a(n) = (4/45)*n*(n - 2)*(n - 1)*(n^3 - 12*n^2 + 47*n - 15).
4
0, 0, 0, 24, 96, 240, 544, 1288, 3136, 7392, 16320, 33528, 64416, 116688, 200928, 331240, 525952, 808384, 1207680, 1759704, 2508000, 3504816, 4812192, 6503112, 8662720, 11389600, 14797120, 19014840, 24189984, 30488976, 38099040, 47229864, 58115328, 71015296
OFFSET
0,4
FORMULA
a(n) = [x^6] JacobiTheta3(x)^n.
a(n) = A319574(n,6).
From Colin Barker, Oct 02 2018: (Start)
G.f.: 8*x^3*(3 - 9*x + 9*x^2 + 5*x^3) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6.
(End)
MAPLE
a := n -> (4/45)*n*(n - 2)*(n - 1)*(n^3 - 12*n^2 + 47*n - 15):
seq(a(n), n=0..41);
MATHEMATICA
A319577[n_]:=4/45*n*(n-2)*(n-1)*(n^3-12*n^2+47*n-15); Array[A319577, 50, 0] (*or*)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 24, 96, 240, 544}, 50] (* Paolo Xausa, Feb 20 2024 *)
PROG
(PARI) concat([0, 0, 0], Vec(8*x^3*(3 - 9*x + 9*x^2 + 5*x^3) / (1 - x)^7 + 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), A319576 (m=5), this sequence (m=6).
Column n=6 of A122141.
Cf. A319574.
Sequence in context: A195824 A183009 A272871 * A277563 A225790 A042122
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Oct 01 2018
STATUS
approved