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 A143167 #16 Jan 09 2019 21:23:10 %S A143167 1,9,111,1785,35595,848925,23586255,748471185,26715409875, %T A143167 1059544210725,46230843633975,2201008238854425,113546715232225275, %U A143167 6309834090304870125,375777507964741257375,23876826206710426574625,1612323634555365676819875 %N A143167 Second column of triangle A000369: |S2(-3;n+2,2)|. %H A143167 Robert Israel, <a href="/A143167/b143167.txt">Table of n, a(n) for n = 0..364</a> %F A143167 a(n) = A000369(n+2,2) = |S2(-3;n+2,2)|, n >= 0. %F A143167 E.g.f.: d^2/dx^2 ((1-(1-4*x)^(1/4))^2 )/2! = (3 - 2*(1-4*x)^(1/4))/(1-4*x)^(7/4). %F A143167 From _Robert Israel_, Jan 09 2019: (Start) %F A143167 a(n) = (8*n+1)*a(n-1) - 2*(4*n-1)*(2*n-1)*a(n-2). %F A143167 a(n) = 4^(n+1)*(Gamma(n+7/4)/Gamma(3/4) - Gamma(n+3/2)/Gamma(1/2)). (End) %p A143167 f:= gfun:-rectoproc({a(n) = (8*n+1)*a(n-1) - 2*(4*n-1)*(2*n-1)*a(n-2),a(0)=1, a(1)=9}, a(n), remember): %p A143167 map(f, [$0..50]); # _Robert Israel_, Jan 09 2019 %o A143167 (PARI) x = 'x + O('x^40); serlaplace((3 - 2*(1-4*x)^(1/4))/(1-4*x)^(7/4)) \\ _Michel Marcus_, Jun 18 2017 %Y A143167 First column of A000369 is A008545, third one is A143168. %K A143167 nonn,easy %O A143167 0,2 %A A143167 _Wolfdieter Lang_, Sep 15 2008