OFFSET
0,3
FORMULA
a(n+1) = Sum{k, 0<=k<=n} 8^k*A113129(n, k).
G.f.: A(x) = x/series_reversion(x*G(x)) where G(x) = g.f. of 8-fold factorials.
G.f. satisfies: A(x*G(x)) = G(x) = g.f. of 8-fold factorials.
EXAMPLE
a(2) = 8.
a(3) = 2*8^2 = 128.
a(4) = 8*3*128 + 1*8*8 = 3136.
a(5) = 8*4*3136 + 1*8*128 + 2*128*8 = 103424.
a(6) = 8*5*103424 + 1*8*3136 + 2*128*128 + 3*3136*8 = 4270080
G.f.: A(x) = 1 + x + 8*x^2 + 128*x^3 + 3136*x^4 + 103424*x^5 +...
= x/series_reversion(x + x^2 + 9*x^3 + 153*x^4 + 3825*x^5 +...).
MATHEMATICA
x=8; a[0]=a[1]=1; a[2]=x; a[3]=2x^2; a[n_]:=a[n]=x*(n-1)*a[n-1]+Sum[(j-1)*a[j ]*a[n-j], {j, 2, n-2}]; Table[a[n], {n, 0, 16}](Robert G. Wilson v)
PROG
(PARI) a(n)=Vec(x/serreverse(x*Ser(vector(n+1, k, if(k==1, 1, prod(j=0, k-2, 8*j+1))))))[n+1]
(PARI) a(n, x=8)=if(n<0, 0, if(n==0 || n==1, 1, if(n==2, x, if(n==3, 2*x^2,
x*(n-1)*a(n-1)+sum(j=2, n-2, (j-1)*a(j)*a(n-j))))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham and Paul D. Hanna, Oct 28 2005
STATUS
approved