A344401 a(n) = [x^n] 24*(-40*x^4 + 49*x^3 - 15*x^2 + 13*x + 2) / (1 - 4*x)^(9/2).

48, 1176, 14760, 138840, 1102080, 7814016, 51104592, 314542800, 1846484640, 10435991280, 57176069808, 305224906896, 1593937712640, 8168132011200, 41177443370400, 204627619798560, 1004073535314720, 4871589672747600, 23398711748319600, 111369179635837200

Offset: 0

Author

Peter Luschny, May 16 2021

Keywords

• nonn

Comments

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

Links

• Peter Luschny, Remark regarding A344228 and A344321.

Crossrefs

Cf. A344400, A344228, A344321.

Programs

Maple

aList := proc(len) local gf, ser;
   gf := 24*(-40*x^4 + 49*x^3 - 15*x^2 + 13*x + 2) / (1 - 4*x)^(9/2):
   ser := series(gf, x, len+2): seq(coeff(ser, x, n), n = 0..len) end:
aList(19);

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

Formula

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