A341197
a(n) = Sum_{k=0..n} k^n * (n-k)! * binomial(n,k)^2.
Original entry on oeis.org
1, 1, 8, 117, 2800, 97125, 4551876, 274975897, 20690260928, 1889451727497, 205192914235300, 26068434774065541, 3822244304373085680, 639508508456359098349, 120922358829574588363364, 25626415609908102483018225
Offset: 0
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a[0] = 1; a[n_] := Sum[k^n * (n-k)! * Binomial[n, k]^2, {k, 0, n}]; Array[a, 16, 0] (* Amiram Eldar, Feb 06 2021 *)
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a(n) = sum(k=0, n, k^n*(n-k)!*binomial(n, k)^2);
A341196
a(n) = Sum_{k=0..n} k^4 * (n-k)! * binomial(n,k)^2.
Original entry on oeis.org
0, 1, 20, 243, 2800, 33425, 424116, 5762155, 83891648, 1306561185, 21709011700, 383654149571, 7189789929840, 142465285362673, 2976697773182420, 65417312929686075, 1508567496105346816, 36425941390897897025, 919100609186531702868
Offset: 0
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a[n_] := Sum[k^4 * (n-k)! * Binomial[n, k]^2, {k, 0, n}]; Array[a, 19, 0] (* Amiram Eldar, Feb 06 2021 *)
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a(n) = sum(k=0, n, k^4*(n-k)!*binomial(n, k)^2);
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(x*(1+4*x-5*x^2+x^3)*exp(x/(1-x))/(1-x)^5)))
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