This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A361545 #16 Aug 28 2025 05:02:51
%S A361545 1,0,0,0,1,5,30,210,1715,15750,160650,1801800,22043175,292116825,
%T A361545 4168464300,63725161500,1039028615625,17998106626500,330068683444500,
%U A361545 6388785205803000,130156170633113625,2783924007745505625,62375052003905891250,1460924768552182683750
%N A361545 Expansion of e.g.f. exp(x^4/(24 * (1-x))).
%F A361545 a(n) = 2*(n-1) * a(n-1) - (n-1)*(n-2) * a(n-2) + binomial(n-1,3) * a(n-4) - 3*binomial(n-1,4) * a(n-5) for n > 4.
%F A361545 From _Seiichi Manyama_, Jun 17 2024: (Start)
%F A361545 a(n) = n! * Sum_{k=0..floor(n/4)} binomial(n-3*k-1,n-4*k)/(24^k * k!).
%F A361545 a(0) = 1; a(n) = ((n-1)!/24) * Sum_{k=4..n} k * a(n-k)/(n-k)!. (End)
%F A361545 a(n) ~ 2^(-5/4) * 3^(-1/4) * exp(-7/48 + sqrt(n/6) - n) * n^(n - 1/4). - _Vaclav Kotesovec_, Aug 28 2025
%t A361545 RecurrenceTable[{3 (-4 + n) (-3 + n) (-2 + n) (-1 + n) a[-5 + n] - 4 (-3 + n) (-2 + n) (-1 + n) a[-4 + n] + 24 (-2 + n) (-1 + n) a[-2 + n] - 48 (-1 + n) a[-1 + n] + 24 a[n] == 0, a[1] == 0, a[2] == 0, a[3] == 0, a[4] == 1, a[5] == 5}, a, {n, 0, 25}] (* _Vaclav Kotesovec_, Aug 28 2025 *)
%o A361545 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^4/(24*(1-x)))))
%Y A361545 Cf. A185369, A361533, A361547.
%Y A361545 Cf. A293050.
%K A361545 nonn,changed
%O A361545 0,6
%A A361545 _Seiichi Manyama_, Mar 15 2023