OFFSET
0,3
FORMULA
EXAMPLE
a(2) = 5.
a(3) = 2*5^2 = 50.
a(4) = 5*3*50 + 1*5*5 = 775.
a(5) = 5*4*775 + 1*5*50 + 2*50*5 = 16250.
a(6) = 5*5*16250 + 1*5*775 + 2*50*50 + 3*775*5 = 426750.
G.f.: A(x) = 1 + x + 5*x^2 + 50*x^3 + 775*x^4 + 16250*x^5 +...
= x/series_reversion(x + x^2 + 6*x^3 + 66*x^4 + 1056*x^5
+...).
MATHEMATICA
x=5; 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, 17}](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, 5*j+1))))))[n+1]
(PARI) a(n, x=5)=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