A291450 Denominators of Integral_{x=0..1} P(n, x)^3 with P(n, x) = Sum_{k=0..n}(-1)^(n-k)* Stirling2(n, k)*k!*x^k.

1, 4, 140, 28, 20020, 4004, 6466460, 184756, 148728580, 29745716, 133706993420, 2431036244, 449741705140, 31885268, 670910837521540, 134182167504308, 409926521725660940, 4822664961478364, 1278006214791766460, 1921813856829724, 242081282475556183660, 4401477863191930612

Offset: 0

Author

Peter Luschny, Aug 24 2017

Keywords

• nonn
• frac

Comments

See A291449 and A290694 for comments.

Crossrefs

Cf. A164555/A027642, A212196/A181131, A291449/A291450, A290694/A290695, A291447/A291448.

Programs

Maple

# Function BG_row is defined in A290694.
seq(BG_row(3, n, "den", "val"), n=0..20);

Mathematica

P[n_, x_] := Sum[(-1)^(n-k)*StirlingS2[n, k]*k!*x^k, {k, 0, n}];
a[n_] := Integrate[P[n, x]^3, {x, 0, 1}] // Denominator;
Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jun 15 2019 *)