A367374 Expansion of the e.g.f. (exp(x) / (5 - 4*exp(x)))^(2/5).
1, 2, 12, 128, 1944, 38264, 924936, 26507672, 878565000, 33058419032, 1392125985864, 64864749910424, 3313075222410504, 184071465908101592, 11051901784679926728, 713107430713993422872, 49208366812318404125832, 3616200105869781814285400
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, (-1)^(n-k)*prod(j=0, k-1, 5*j+2)*stirling(n, k, 2));
Formula
a(n) = Sum_{k=0..n} (-1)^(n-k) * (Product_{j=0..k-1} (5*j+2)) * Stirling2(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^k * (3*k/n - 5) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = 2*a(n-1) + 4*Sum_{k=1..n-1} binomial(n-1,k) * a(n-k).