OFFSET
0,5
FORMULA
E.g.f.: exp( (x / (1-x))^4 ).
a(n) = n! * Sum_{k=0..floor(n/4)} binomial(n-1,n-4*k)/k!.
a(0) = 1; a(n) = (n-1)! * Sum_{k=4..n} (-1)^(k-4) * k * binomial(-4,k-4) * a(n-k)/(n-k)!.
a(n) = 5*(n-1)*a(n-1) - 10*(n-2)*(n-1)*a(n-2) + 10*(n-3)*(n-2)*(n-1)*a(n-3) - (n-3)*(n-2)*(n-1)*(5*n - 24)*a(n-4) + (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5). - Vaclav Kotesovec, Mar 17 2023
MATHEMATICA
Table[n! * Sum[Binomial[n-1, n-4*k]/k!, {k, 0, n/4}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 17 2023 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp((x/(1-x))^4)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=4, i, (-1)^(j-4)*j*binomial(-4, j-4)*v[i-j+1]/(i-j)!)); v;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 16 2023
STATUS
approved