A373433 a(n) = A000111(n) * A000142(n). Row sums of A373434.

1, 1, 2, 12, 120, 1920, 43920, 1370880, 55843200, 2879815680, 183330604800, 14122244505600, 1294628759424000, 139287595371724800, 17379949655535667200, 2489494639794978816000, 405724534220435189760000, 74646464089618378653696000, 15396938399483145082626048000

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

a(n) = n! * 2^n * |Euler(n, 1/2) + Euler(n, 1)| for n >= 1.

a(n) ~ ((2*n^2)/(Pi*e^2))^n*(8*n + 4/3).

Maple

A373433 := n -> ifelse(n = 0, 1, n! * 2^n * abs(euler(n, 1/2) + euler(n, 1))):
seq(A373433(n), n = 0..18);

Mathematica

A373433[n_] := 2 I^(n + 1) n! PolyLog[-n, -I]; A373433[0] := 1;
Table[A373433[n], {n, 0, 18}]

Prog

(SageMath)  # Algorithm of Ludwig Seidel (1877).
def A373433_list(n) :
    R = []; S = []; A = {-1:0, 0:1}; k = 0; f = 1; e = 1
    for i in (0..n) :
        Am = 0; A[k + e] = 0; e = -e
        for j in (0..i) : Am += A[k]; A[k] = Am; k += e
        R.append(Am); S.append(f*Am); f *= i + 1
    return S
print(A373433_list(18))

Crossrefs

Cf. A000111, A000142, A373434.

Sequence in context: A048800 A251185 A052738 * A229901 A007132 A138534

Adjacent sequences: A373430 A373431 A373432 * A373434 A373435 A373436

Keyword

nonn

Author

Peter Luschny, Jun 04 2024

Status

approved