A377959 Expansion of e.g.f. exp(x - x^2)/(1 - x)^2.
1, 3, 9, 31, 141, 831, 5773, 45459, 403161, 3990331, 43544721, 518940423, 6706062949, 93404895351, 1394851282581, 22230473112571, 376610264357553, 6758060929028979, 128047472471583001, 2554547113522500591, 53523844242070603581, 1175091669834676927663
Offset: 0
Keywords
Programs
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PARI
a(n) = n!*sum(k=0, n, binomial(n-2*k+1, n-k)/k!);
Formula
a(n) = n! * Sum_{k=0..n} binomial(n-2*k+1,n-k) / k!.
a(n) = (n+2)*a(n-1) - 3*(n-1)*a(n-2) + 2*(n-1)*(n-2)*a(n-3) for n > 2.