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 A361547 #19 Aug 28 2025 05:57:01
%S A361547 1,0,0,0,0,1,6,42,336,3024,30366,335412,4041576,52756704,741620880,
%T A361547 11169844686,179448036768,3063069801792,55360031126400,
%U A361547 1056123043335360,21208345049147256,447183762148547424,9877939209960101280,228112734232663600320
%N A361547 Expansion of e.g.f. exp(x^5/(120 * (1-x))).
%C A361547 In general, if m>=1 and e.g.f. = exp(x^m / (m! * (1-x))), then a(n) ~ n! * exp(2*sqrt(n/m!) - (2*m-1)/(2*m!)) / (2*sqrt(Pi) * m!^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Aug 28 2025
%F A361547 a(n) = 2*(n-1) * a(n-1) - (n-1)*(n-2) * a(n-2) + binomial(n-1,4) * a(n-5) - 4*binomial(n-1,5) * a(n-6) for n > 5.
%F A361547 From _Seiichi Manyama_, Jun 17 2024: (Start)
%F A361547 a(n) = n! * Sum_{k=0..floor(n/5)} binomial(n-4*k-1,n-5*k)/(120^k * k!).
%F A361547 a(0) = 1; a(n) = ((n-1)!/120) * Sum_{k=5..n} k * a(n-k)/(n-k)!. (End)
%F A361547 a(n) ~ 2^(-5/4) * 15^(-1/4) * exp(-3/80 + sqrt(n/30) - n) * n^(n - 1/4). - _Vaclav Kotesovec_, Aug 28 2025
%t A361547 RecurrenceTable[{4 (-5 + n) (-4 + n) (-3 + n) (-2 + n) (-1 + n) a[-6 + n] - 5 (-4 + n) (-3 + n) (-2 + n) (-1 + n) a[-5 + n] + 120 (-2 + n) (-1 + n) a[-2 + n] - 240 (-1 + n) a[-1 + n] + 120 a[n] == 0, a[1] == 0, a[2] == 0, a[3] == 0, a[4] == 0, a[5] == 1, a[6] == 6}, a, {n, 0, 25}] (* _Vaclav Kotesovec_, Aug 28 2025 *)
%o A361547 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x^5/(120*(1-x)))))
%Y A361547 Cf. A185369, A361533, A361545.
%K A361547 nonn,changed
%O A361547 0,7
%A A361547 _Seiichi Manyama_, Mar 15 2023