A344400 a(n) = [x^n] 6*(8*x^3 + 3*x + 1) / (1 - 4*x)^(7/2).

6, 102, 1008, 7860, 53340, 330372, 1918224, 10615176, 56602260, 293032740, 1481004096, 7337198232, 35743534008, 171641101800, 814046047200, 3819148459920, 17747499595140, 81776562767460, 373968175442400, 1698587342436600, 7667851012141320, 34422129328312440

Offset: 0

Author

Peter Luschny, May 16 2021

Keywords

• nonn

Comments

The sequence and its sister sequence A344401 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. A344401, A344228, A344321.

Programs

Maple

aList := proc(len) local gf, ser;
   gf := 6*(8*x^3 + 3*x + 1) / (1 - 4*x)^(7/2):
   ser := series(gf, x, len+2): seq(coeff(ser, x, n), n = 0..len) end:
aList(21);

Formula

a(n) = A344228(n+1)*(n+1)*(n+2). - John Keith, May 23 2021