A383842 Expansion of 1/((1-x) * (1-2*x) * (1-3*x) * (1-4*x))^2.

1, 20, 230, 2000, 14627, 95060, 567240, 3174400, 16904053, 86549620, 429352330, 2075659600, 9822847079, 45665147700, 209129160300, 945597624000, 4229196800505, 18738054705300, 82347219011950, 359322115058000, 1558151553849131, 6719660438870420, 28838298857544080

Offset: 0

Author

Seiichi Manyama, May 12 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (20,-170,800,-2273,3980,-4180,2400,-576).

Crossrefs

Column k=4 of A383843.

Cf. A000453.

Programs

PARI

a(n) = sum(k=0, n, stirling(k+4, 4, 2)*stirling(n-k+4, 4, 2));

Formula

a(n) = 20*a(n-1) - 170*a(n-2) + 800*a(n-3) - 2273*a(n-4) + 3980*a(n-5) - 4180*a(n-6) + 2400*a(n-7) - 576*a(n-8).

a(n) = Sum_{k=0..n} Stirling2(k+4,4) * Stirling2(n-k+4,4).