A379994 Expansion of e.g.f. exp(-3*x)/(exp(-x) - x)^4.
1, 5, 37, 349, 3969, 52641, 796069, 13502693, 253667297, 5225690017, 117090480021, 2834363683317, 73697918467105, 2048252470006913, 60587779740857573, 1900347489736371301, 62992469337321611073, 2200238756416513719489, 80765631192992760237205
Offset: 0
Programs
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PARI
a(n) = n!*sum(k=0, n, (k+1)^(n-k)*binomial(k+3, 3)/(n-k)!);
Formula
a(n) = n! * Sum_{k=0..n} (k+1)^(n-k) * binomial(k+3,3)/(n-k)!.
a(n) == 1 (mod 4).