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 A028165 #26 Feb 13 2025 07:53:57
%S A028165 1,26,425,5590,64701,688506,6906145,66324830,616252901,5580303586,
%T A028165 49508360265,432061044870,3720287489101,31681154472266,
%U A028165 267320885100785,2238337148081710,18621251375573301,154069635600426546
%N A028165 Expansion of 1/((1-5x)*(1-6x)*(1-7x)*(1-8x)).
%C A028165 This is the column m=2 sequence (without leading zeros) of the Sheffer triangle (exp(5*x), exp(x)-1) of the 5-restricted Stirling2 numbers A193685. For a proof see the column o.g.f. formula there. - _Wolfdieter Lang_, Oct 07 2011
%H A028165 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (26, -251, 1066, -1680).
%F A028165 If we define f(m,j,x) = Sum_{k=j..m} binomial(m,k)*Stirling2(k,j)*x^(m-k) then a(n-3) = f(n,3,5), (n >= 3). - _Milan Janjic_, Apr 26 2009
%F A028165 a(n) = 26*a(n-1) - 251*a(n-2) + 1066*a(n-3) - 1680*a(n-4), n >= 4. - _Vincenzo Librandi_, Mar 19 2011
%F A028165 a(n) = 15*a(n-1) - 56*a(n-2) + 6^(n+1) - 5^(n+1), a(0)=1, a(1)=26. - _Vincenzo Librandi_, Mar 19 2011
%F A028165 E.g.f.: (d^3/dx^3)(exp(5*x)*((exp(x)-1)^3)/3!). See the Sheffer triangle comment above. - _Wolfdieter Lang_, Oct 07 2011
%F A028165 a(n) = -125*5^n/6 + 108*6^n - 343*7^n/2 + 256*8^n/3. - _R. J. Mathar_, Jun 23 2013
%o A028165 (PARI) Vec(1/((1-5*x)*(1-6*x)*(1-7*x)*(1-8*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%Y A028165 Cf. A000351, A005062, A019757, A193685.
%Y A028165 Cf. A000453, A025211, A028025, A003468, A028200, A016109, A016075, A016094.
%K A028165 nonn,easy
%O A028165 0,2
%A A028165 _N. J. A. Sloane_