A254927 Coefficient of x^n in Product_{k=0..n} (1+k*x)^k.

1, 8, 238, 15715, 1822678, 327061056, 83839010860, 29063729300694, 13090011332041111, 7428850394493811712, 5185703819680371737432, 4366227375438927437584444, 4363140133466727238167744916, 5104897162398639619205564019232, 6912594322573705179830176812524216

Offset: 1

Author

Vaclav Kotesovec, Feb 10 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A129256, A008485, A120295.

Programs

Mathematica

Table[Coefficient[Expand[Product[(1+k*x)^k,{k,0,n}]],x^n],{n,1,20}] (* or *)
p=1; Table[p=Expand[p*(1+n*x)^n]; Coefficient[p,x^n],{n,1,20}] (* faster *)

Formula

a(n) ~ exp(n+3/8) * n^(2*n-1/2) / (sqrt(2*Pi) * 3^n).