cp's OEIS Frontend

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.

A294215 E.g.f.: exp(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) - 1).

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%I A294215 #20 Dec 02 2021 16:17:03
%S A294215 1,1,5,31,265,2501,29461,383755,5721521,93393865,1683745381,
%T A294215 32835673751,693498302905,15671281854541,378500195728565,
%U A294215 9704429057721091,263513260349418721,7544370749942882705,227236831102901587141,7177550671651275241615
%N A294215 E.g.f.: exp(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)) - 1).
%H A294215 Seiichi Manyama, <a href="/A294215/b294215.txt">Table of n, a(n) for n = 0..427</a>
%F A294215 a(n+16) = (n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(n+7)*(n+8)*(n+9)*(n+10)*(n+11)*(n+12)*(n+13)*(n+14)*(n+15)*n*a(n) - (n+15)*(n+14)*(n+13)*(n+12)*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)*a(n+2) - 2*(n+15)*(n+14)*(n+13)*(n+12)*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*a(n+3) - 2*(n+15)*(n+14)*(n+13)*(n+12)*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+6)*(n+5)*(n+4)*a(n+4) + 2*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+6)*(n+5)*(n+15)*(n+14)*(n+13)*(n+12)*a(n+5) + 3*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+6)*(n+15)*(n+14)*(n+13)*(n+12)*a(n+6) + 4*(n+11)*(n+10)*(n+9)*(n+8)*(n+7)*(n+15)*(n+14)*(n+13)*(n+12)*a(n+7) - 4*(n+11)*(n+10)*(n+9)*(n+15)*(n+14)*(n+13)*(n+12)*a(n+9) - (n+15)*(n+14)*(n+13)*(n+12)*(n+11)*(3*n+20)*a(n+10) - (2*n+11)*(n+15)*(n+14)*(n+13)*(n+12)*a(n+11) + 2*(n+19)*(n+15)*(n+14)*(n+13)*a(n+12) + 2*(n+15)*(n+14)*(n+17)*a(n+13) + (n+18)*(n+15)*a(n+14) + a(n+15). - _Robert Israel_, Mar 12 2020
%F A294215 a(n) ~ exp(-68413/92160 + 295*n^(1/5) / (192*6^(4/5)) + 15*3^(2/5)*n^(2/5) / (32*2^(3/5)) + 5*n^(3/5) / (4*6^(2/5)) + 5*n^(4/5) / (4*6^(1/5)) - n) * n^(n - 1/10) / (sqrt(5) * 6^(1/10)) * (1 + 18025/(18432*6^(1/5)*n^(1/5))). - _Vaclav Kotesovec_, Dec 02 2021
%t A294215 With[{nn=20},CoefficientList[Series[Exp[1/((1-x)(1-x^2)(1-x^3)(1-x^4))-1],{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Sep 08 2019 *)
%o A294215 (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))-1)))
%Y A294215 Column k=4 of A294212.
%K A294215 nonn
%O A294215 0,3
%A A294215 _Seiichi Manyama_, Oct 25 2017