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%I #10 Sep 08 2022 08:46:21
%S 41,1513,19689,175465,1287657,8420713,51126249,295141225,1644285417,
%T 8927926633,47563308009,249806529385,1297882995177,6687496584553,
%U 34237868091369,174415093507945,885051189224937,4477377106010473,22596025278436329,113818651291052905
%N a(n) = 6144*5^n - 12288*4^n + 7616*3^n - 1472*2^n + 41.
%H Takao Komatsu, <a href="https://arxiv.org/abs/1806.05515">On poly-Euler numbers of the second kind</a>, arXiv:1806.05515 [math.NT], 2018, page 11 (Lemma 3.4).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (15,-85,225,-274,120).
%F G.f.: (41 + 898*x + 479*x^2 - 490*x^3 + 56*x^4)/((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)).
%F a(n) = 15*a(n-1) - 85*a(n-2) + 225*a(n-3) - 274*a(n-4) + 120*a(n-5) for n>5.
%t Table[6144 5^n - 12288 4^n + 7616 3^n - 1472 2^n + 41, {n, 0, 30}]
%o (Magma) [6144*5^n-12288*4^n+7616*3^n-1472*2^n+41: n in [0..20]];
%Y Cf. A007051, A081188, A305861, A305862.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Jul 04 2018