A383137 a(n) = Sum_{k=0..n} k^3 * 2^(n-k) * binomial(n,k).

0, 1, 12, 87, 504, 2565, 11988, 52731, 221616, 898857, 3542940, 13640319, 51490728, 191141613, 699376356, 2527001955, 9030245472, 31955015889, 112093661484, 390132432423, 1348223301720, 4629287423061, 15802106905332, 53651151578187, 181257000301584

Offset

0,3

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12,-54,108,-81).

Formula

a(n) = 3^(n-3) * n * (2 + 6*n + n^2).

G.f.: x*(1 - 3*x^2)/(1 - 3*x)^4. - Andrew Howroyd, Nov 12 2025

From Enrique Navarrete, Dec 02 2025: (Start)

a(n) = 12*a(n-1) - 54*a(n-2) + 108*a(n-3) - 81*a(n-4).

E.g.f.: (x^3 + 3*x^2 + x)*exp(3*x). (End)

Prog

(PARI) a(n) = 3^(n-3)*n*(2+6*n+n^2);

Crossrefs

Cf. A027471, A383136, A383138, A383139.

Sequence in context: A243248 A046023 A369421 * A183721 A180797 A137207

Adjacent sequences: A383134 A383135 A383136 * A383138 A383139 A383140

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 17 2025

Status

approved