A383151 a(n) = Sum_{k=0..n} k^4 * (-1)^k * 3^(n-k) * binomial(n,k).
0, -1, 10, 36, 40, -160, -1152, -4480, -13568, -34560, -74240, -123904, -92160, 425984, 2867200, 11796480, 40763392, 128122880, 378667008, 1070858240, 2928148480, 7795113984, 20300431360, 51900317696, 130610626560, 324219699200, 795206483968, 1929715384320
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..700
Programs
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Magma
[&+[k^4 * (-1)^k * 3^(n-k) * Binomial(n,k): k in [0..n]]: n in [0..29]]; // Vincenzo Librandi, Apr 23 2025
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Mathematica
Table[Sum[(k^4*(-1)^k*3^(n-k))*Binomial[n,k],{k,0,n}],{n,0,30}] (* Vincenzo Librandi, Apr 23 2025 *) -
PARI
a(n) = 2^(n-4)*(-66*n+75*n^2-18*n^3+n^4);
Formula
a(n) = 2^(n-4) * (-66*n + 75*n^2 - 18*n^3 + n^4).