A392727 Expansion of Sum_{k>=0} x^(2*k) / Product_{j=1..3*k} (1 - j * x).

1, 0, 1, 6, 26, 111, 568, 3657, 27008, 211170, 1715023, 14649558, 133591427, 1304656188, 13536385282, 147608591505, 1679480834606, 19885453999167, 244974162781558, 3139818022298838, 41820496710016013, 577626078903470580, 8253537964041122533

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n) = Sum_{k=0..floor(n/2)} Stirling2(n+k,3*k).

Mathematica

Table[Sum[StirlingS2[n + k, 3*k], {k, 0, Floor[n/2]}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 21 2026 *)

Prog

(PARI) a(n) = sum(k=0, n\2, stirling(n+k, 3*k, 2));
(Magma) [&+[StirlingSecond(n+k, 3*k): k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Feb 20 2026

Crossrefs

Cf. A143815, A392726.

Sequence in context: A145374 A289789 A124465 * A287806 A164549 A283341

Adjacent sequences: A392724 A392725 A392726 * A392728 A392729 A392730

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 21 2026

Status

approved