OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Bell Polynomial.
FORMULA
a(0) = 1; a(n) = -(n-1)! * Sum_{k=1..min(4,n)} binomial(3,k-1) * a(n-k)/(n-k)!.
a(n) = Sum_{k=0..n} 4^k * Stirling1(n,k) * Bell_k(-1/4), where Bell_n(x) is n-th Bell polynomial.
D-finite with recurrence a(n) +a(n-1) +3*(n-1)*a(n-2) +3*(n-1)*(n-2)*a(n-3) +(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Feb 02 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((1-(1+x)^4)/4)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jan 31 2024
STATUS
approved