A344401 - OEIS

%I #16 May 29 2021 05:51:43

%S 48,1176,14760,138840,1102080,7814016,51104592,314542800,1846484640,

%T 10435991280,57176069808,305224906896,1593937712640,8168132011200,

%U 41177443370400,204627619798560,1004073535314720,4871589672747600,23398711748319600,111369179635837200

%N a(n) = [x^n] 24*(-40*x^4 + 49*x^3 - 15*x^2 + 13*x + 2) / (1 - 4*x)^(9/2).

%C The sequence and its sister sequence A344400 are related to Frédéric Chapoton's sequences A344228 and A344321, as described in the linked remark.

%H Peter Luschny, <a href="/A344400/a344400.pdf">Remark regarding A344228 and A344321</a>.

%F 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 aList := proc(len) local gf, ser;

%p    gf := 24*(-40*x^4 + 49*x^3 - 15*x^2 + 13*x + 2) / (1 - 4*x)^(9/2):

%p    ser := series(gf, x, len+2): seq(coeff(ser, x, n), n = 0..len) end:

%p aList(19);

%o (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 Cf. A344400, A344228, A344321.

%K nonn

%O 0,1

%A _Peter Luschny_, May 16 2021