A383841 Expansion of 1/((1-x) * (1-2*x) * (1-3*x))^2.

1, 12, 86, 480, 2307, 10044, 40792, 157440, 584693, 2107596, 7420218, 25634880, 87207559, 292924668, 973531964, 3206704800, 10482373305, 34042285260, 109930177630, 353238247200, 1130137576331, 3601849005372, 11440208166816, 36225346150080, 114391746903037, 360325587293004

Offset: 0

Author

Seiichi Manyama, May 12 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (12,-58,144,-193,132,-36).

Crossrefs

Column k=3 of A383843.

Cf. A000392, A045618.

Programs

PARI

a(n) = sum(k=0, n, stirling(k+3, 3, 2)*stirling(n-k+3, 3, 2));

Formula

a(n) = 12*a(n-1) - 58*a(n-2) + 144*a(n-3) - 193*a(n-4) + 132*a(n-5) - 36*a(n-6).

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