A373772 - OEIS

%I #8 Jun 18 2024 10:01:59

%S 1,1,2,7,32,180,1210,9450,84000,836920,9234400,111742400,1471023400,

%T 20925905000,319830310800,5226116295400,90906373958400,

%U 1676967192700800,32697692264036800,671856896755844800,14509136903381120000,328520930667097168000

%N Expansion of e.g.f. exp(x^3 / (6 * (1 - x))) / (1 - x).

%F a(n) = n! * Sum_{k=0..floor(n/3)} binomial(n-2*k,n-3*k)/(6^k * k!).

%o (PARI) a(n) = n!*sum(k=0, n\3, binomial(n-2*k, n-3*k)/(6^k*k!));

%Y Cf. A130906, A361597, A373773.

%Y Cf. A000930, A361533.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 18 2024