STATUS
reviewed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
reviewed
approved
proposed
reviewed
editing
proposed
T(n,0) = A177253(n).
Sum_{k>=0} k*a(n,k) = (n-3)! (n >= 4).
T(n,k) = Sum_{j=0..floor(n/4)} (-1)^(k+j)*binomial(j,k)*(n-3j3*j)!/j!.
T(n,0) = A177253(n).
Sum_{k>=0} k*T(n,k) = (n-3)! (n >= 4).
T[n_, k_] := T[n, k] = Sum[(-1)^(k + j)*Binomial[j, k]*(n - 3 j)!/j!, {j, 0, n/4}];
(Magma)
A177252:= func< n, k | (&+[(-1)^j*Factorial(n-3*k-3*j)/(Factorial(k) *Factorial(j)): j in [0..Floor((n-4*k)/4)]]) >;
[A177252(n, k): k in [0..Floor(n/4)], n in [0..20]]; // G. C. Greubel, Apr 28 2024
(SageMath)
def A177252(n, k): return sum((-1)^j*factorial(n-3*k-3*j)/(factorial(k) *factorial(j)) for j in range(1+(n-4*k)//4))
flatten([[A177252(n, k) for k in range(1+n//4)] for n in range(21)]) # G. C. Greubel, Apr 28 2024
Cf. A000142 (row sums).
approved
editing
proposed
approved
editing
proposed
Seiichi Manyama, <a href="/A177252/b177252_1.txt">Rows n = 0..200, flattened</a>
reviewed
approved
proposed
reviewed