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%I #8 Dec 31 2023 10:22:13
%S 0,1,2,4,4,15,-34,322,-2456,22269,-222470,2447456,-29369108,381798859,
%T -5345183466,80177752670,-1282844041904,21808348713337,
%U -392550276838926,7458455259940924,-149169105198816940,3132551209175157511,-68916126601853463218
%N a(n) = n! * Sum_{k=0..n} (-1)^(n-k) * binomial(k+2,3) / k!.
%F a(0) = 0; a(n) = -n*a(n-1) + binomial(n+2,3).
%F E.g.f.: x * (1+x+x^2/6) * exp(x) / (1+x).
%o (PARI) my(N=30, x='x+O('x^N)); concat(0, Vec(serlaplace(x*sum(k=0, 2, binomial(2, k)*x^k/(k+1)!)*exp(x)/(1+x))))
%Y Cf. A009574, A368586, A368587.
%Y Cf. A368574.
%K sign,easy
%O 0,3
%A _Seiichi Manyama_, Dec 31 2023
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