A343561 2nd row of A341867: a(n) = (n^2+15*n+32)*2^(n-3).

4, 12, 33, 86, 216, 528, 1264, 2976, 6912, 15872, 36096, 81408, 182272, 405504, 897024, 1974272, 4325376, 9437184, 20512768, 44433408, 95944704, 206569472, 443547648, 950009856, 2030043136, 4328521728, 9210691584, 19562233856, 41473277952, 87778394112, 185488900096

Offset

0,1

Links

Jianing Song, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Formula

a(n) = Sum_{k=0..n} binomial(n,k) * (k^2+7*k+8)/2.

G.f.: (2 - 3*x)^2/(1 - 2*x)^3.

E.g.f.: exp(2*x) * (x^2/2 + 4*x + 4).

Mathematica

a[n_] := (n^2 + 15*n + 32)*2^(n - 3); Array[a, 31, 0] (* Amiram Eldar, Nov 08 2021 *)

Prog

(PARI) a(n) = (n^2+15*n+32)*2^(n-3)

Crossrefs

Cf. A341867.

Sequence in context: A318637 A227554 A305778 * A104747 A070050 A186025

Adjacent sequences: A343558 A343559 A343560 * A343562 A343563 A343564

Keyword

nonn,easy

Author

Jianing Song, Nov 07 2021

Status

approved