OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..409
FORMULA
a(n)= sum(A134141(n,m),m=1..n),n>=1.
E.g.f.: exp((1-(1-x)^6)/(6*(1-x)^6)). Cf. e.g.f. first column of A134141.
From Seiichi Manyama, Jan 18 2025: (Start)
a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A005012(k).
a(n) = (1/exp(1/6)) * (-1)^n * n! * Sum_{k>=0} binomial(-6*k,n)/(6^k * k!). (End)
MAPLE
a:= proc(n) option remember; `if`(n=0, 1, add(
binomial(n-1, j-1)*(j+5)!/6!*a(n-j), j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Aug 01 2017
MATHEMATICA
a[n_]:=a[n]=If[n==0, 1, Sum[Binomial[n - 1, j - 1] (j + 5)!/6! a[n - j], {j, n}]]; Table[a[n], {n, 0, 25}] (* Indranil Ghosh, Aug 02 2017, after Maple code *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 12 2007
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Aug 01 2017
STATUS
approved