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 A355414 #11 Aug 02 2025 13:41:41
%S A355414 0,1,13,149,1750,21894,295500,4320420,68487120,1176564240,21883528800,
%T A355414 440117949600,9557404012800,223720054790400,5634130146624000,
%U A355414 152315974848038400,4409413104676608000,136318041562123008000,4487618159996944896000,156852415886275726848000,5803748680475885432832000
%N A355414 Expansion of the e.g.f. log((1 - x) / (1 - 2*x)) / (1 - x)^5.
%C A355414 Conjecture: For p prime, a(p) == -1 (mod p).
%F A355414 a(n) = Sum_{k=0..n} (-1)^(k+1)*k!*A062140(n, k+1).
%F A355414 a(0) = 0, a(n) = n!*Sum_{k=1..n} A000332(n-k+4)*(2^k-1)/k.
%F A355414 a(n) = binomial(n+4, 5)*n!*hypergeom([1 - n, 1, 1], [2, 6], -1). - _Peter Luschny_, Jul 01 2022
%F A355414 D-finite with recurrence a(n) +(-4*n-5)*a(n-1) +(n+3)*(5*n-3)*a(n-2) -2*(n-2)*(n+3)*(n+2)*a(n-3)=0. - _R. J. Mathar_, Jul 27 2022
%p A355414 A355414 := proc(n)
%p A355414 n!*binomial(n+4,5)*hypergeom([1-n,1,1],[2,6],-1) ;
%p A355414 simplify(%) ;
%p A355414 end proc:
%p A355414 seq(A355414(n),n=0..40) ; # _R. J. Mathar_, Jul 27 2022
%t A355414 With[{nn=20},CoefficientList[Series[Log[((1-x)/(1-2x))]/(1-x)^5,{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Aug 02 2025 *)
%Y A355414 Cf. A000332, A062140, A355171, A355372, A355407.
%K A355414 nonn
%O A355414 0,3
%A A355414 _Mélika Tebni_, Jul 01 2022