OFFSET
0,2
LINKS
FORMULA
E.g.f.: (1+24*x+84*x^2+56*x^3)/(1-x)^12.
a(n) = A062138(n+3, 3).
a(n) = (n+3)!*binomial(n+8, 8)/3!.
If we define f(n,i,x) = Sum_{k=i..n} Sum_{j=i..k} binomial(k,j) * Stirling1(n,k) * Stirling2(j,i) * x^(k-j) then a(n-3)=(-1)^(n-1)*f(n,3,-9), (n>=3). - Milan Janjic, Mar 01 2009
From Amiram Eldar, Sep 11 2025: (Start)
Sum_{n>=0} 1/a(n) = 301302/35 - 3504*e - 696*gamma + 696*Ei(1), where e = A001113, gamma = A001620, and Ei(1) = A091725.
Sum_{n>=0} (-1)^n/a(n) = -19566/35 - 1440/e + 1368*gamma - 1368*Ei(-1), where Ei(-1) = -A099285. (End)
EXAMPLE
a(2) = (2+3)! * binomial(2+8,8) / 3! = (120 * 45) / 6 = 900. - Indranil Ghosh, Feb 24 2017
MATHEMATICA
Table[(n+3)!*Binomial[n+8, 8]/3!, {n, 0, 15}] (* Indranil Ghosh, Feb 24 2017 *)
PROG
(PARI) a(n)=(n+3)!*binomial(n+8, 8)/3! \\ Indranil Ghosh, Feb 24 2017
(Python)
import math
f=math.factorial
def C(n, r):return f(n)/f(r)/f(n-r)
def A062150(n): return f(n+3)*C(n+8, 8)/f(3) # Indranil Ghosh, Feb 24 2017
(Magma) [Factorial(n+3)*Binomial(n+8, 8)/6: n in [0..20]]; // G. C. Greubel, May 12 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jun 19 2001
STATUS
approved
