A367376 Expansion of the e.g.f. (exp(x) / (5 - 4*exp(x)))^(4/5).
1, 4, 32, 400, 6800, 146128, 3795728, 115616848, 4040024720, 159282704848, 6993908053520, 338443123424080, 17894609985867152, 1026351961130219728, 63466858180767590672, 4209071260503851502160, 298006515851074633361552, 22434758711582422326267856
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+4)*stirling(n, k, 2));
Formula
a(n) = Sum_{k=0..n} (-1)^(n-k) * (Product_{j=0..k-1} (5*j+4)) * Stirling2(n,k).
a(0) = 1; a(n) = Sum_{k=1..n} (-1)^k * (k/n - 5) * binomial(n,k) * a(n-k).
a(0) = 1; a(n) = 4*a(n-1) + 4*Sum_{k=1..n-1} binomial(n-1,k) * a(n-k).