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

0,1

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

Table of n, a(n) for n=0..19.

Peter Luschny, Remark regarding A344228 and A344321.

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

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);

Prog

(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

Crossrefs

Cf. A344400, A344228, A344321.

Sequence in context: A161693 A162193 A162461 * A369561 A011000 A025233

Adjacent sequences: A344398 A344399 A344400 * A344402 A344403 A344404

Keyword

nonn

Author

Peter Luschny, May 16 2021

Status

approved