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 A344401 #16 May 29 2021 05:51:43 %S A344401 48,1176,14760,138840,1102080,7814016,51104592,314542800,1846484640, %T A344401 10435991280,57176069808,305224906896,1593937712640,8168132011200, %U A344401 41177443370400,204627619798560,1004073535314720,4871589672747600,23398711748319600,111369179635837200 %N A344401 a(n) = [x^n] 24*(-40*x^4 + 49*x^3 - 15*x^2 + 13*x + 2) / (1 - 4*x)^(9/2). %C A344401 The sequence and its sister sequence A344400 are related to Frédéric Chapoton's sequences A344228 and A344321, as described in the linked remark. %H A344401 Peter Luschny, <a href="/A344400/a344400.pdf">Remark regarding A344228 and A344321</a>. %F A344401 a(n) = 6*(3*n + 4)*(2*n^3 + 9*n^2 + 13*n + 4)*binomial(2*n-1, n) for n>=1. - _John Keith_, May 28 2021 %p A344401 aList := proc(len) local gf, ser; %p A344401 gf := 24*(-40*x^4 + 49*x^3 - 15*x^2 + 13*x + 2) / (1 - 4*x)^(9/2): %p A344401 ser := series(gf, x, len+2): seq(coeff(ser, x, n), n = 0..len) end: %p A344401 aList(19); %o A344401 (PARI) a(n) = if(n==0, 48, 6*(3*n + 4)*(2*n^3 + 9*n^2 + 13*n + 4)*binomial(2*n-1, n)) \\ _Andrew Howroyd_, May 28 2021 %Y A344401 Cf. A344400, A344228, A344321. %K A344401 nonn %O A344401 0,1 %A A344401 _Peter Luschny_, May 16 2021