A383138 a(n) = Sum_{k=0..n} k^4 * 2^(n-k) * binomial(n,k).

0, 1, 20, 189, 1320, 7785, 41148, 201285, 929232, 4100625, 17452260, 72098829, 290521080, 1146082041, 4439303820, 16923738645, 63619864992, 236206924065, 867305334708, 3152957079645, 11359168737480, 40589657212041, 143957705302620, 507079568653029

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (15,-90,270,-405,243).

Formula

a(n) = 3^(n-4) * n * (-6 + 20*n + 12*n^2 + n^3).

G.f.: x*(1 - x)*(1 + 6*x - 15*x^2)/(1 - 3*x)^5. - Andrew Howroyd, Nov 12 2025

Prog

(PARI) a(n) = 3^(n-4)*n*(-6+20*n+12*n^2+n^3);

Crossrefs

Cf. A027471, A383136, A383137, A383139.

Sequence in context: A177073 A211153 A210429 * A367780 A047645 A010936

Adjacent sequences: A383135 A383136 A383137 * A383139 A383140 A383141

Keyword

nonn,easy

Author

Seiichi Manyama, Apr 17 2025

Status

approved