A354394 - OEIS

%I #10 May 25 2022 09:15:34

%S 1,0,0,0,0,-1,-15,-140,-1050,-6951,-42273,-232870,-949740,2401399,

%T 149618469,2979464124,47639256210,683529622229,9045426379611,

%U 109599657976942,1148191101672384,8033814119097459,-50834295574038207,-3977581842278623216,-119536187842156328034

%N Expansion of e.g.f. 1/(1 + (exp(x) - 1)^5 / 120).

%F a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * Stirling2(k,5) * a(n-k).

%F a(n) = Sum_{k=0..floor(n/5)} (5*k)! * Stirling2(n,5*k)/(-120)^k.

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+(exp(x)-1)^5/120)))

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, binomial(i, j)*stirling(j, 5, 2)*v[i-j+1])); v;

%o (PARI) a(n) = sum(k=0, n\5, (5*k)!*stirling(n, 5*k, 2)/(-120)^k);

%Y Cf. A354391, A354392, A354393.

%Y Cf. A346896, A346924, A354398.

%K sign

%O 0,7

%A _Seiichi Manyama_, May 25 2022