A316526 a(n) = 122880*6^n - 307200*5^n + 264960*4^n - 90240*3^n + 9844*2^n - 122.
122, 9966, 210134, 2741670, 27930182, 245220486, 1953210374, 14543545350, 103166087942, 706033804806, 4702595902214, 30675859444230, 196880387684102, 1247535454225926, 7825081688699654, 48684535015586310, 300917096071974662, 1850113238390115846
Offset: 0
Links
- Takao Komatsu, On poly-Euler numbers of the second kind, arXiv:1806.05515 [math.NT], 2018, page 11 (Lemma 3.4).
- Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).
Programs
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Magma
[122880*6^n-307200*5^n+264960*4^n-90240*3^n+9844*2^n-122: n in [0..20]];
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Mathematica
Table[122880 6^n - 307200 5^n + 264960 4^n - 90240 3^n + 9844 2^n - 122, {n, 0, 20}]
Formula
G.f.: 2*(61 + 3702*x + 11099*x^2 - 8382*x^3 + 840*x^4)/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)).
a(n) = 21*a(n-1) - 175*a(n-2) + 735*a(n-3) - 1624*a(n-4) + 1764*a(n-5) - 720*a(n-6) for n>6.