A084903 Binomial transform of positive cubes.

1, 9, 44, 170, 576, 1792, 5248, 14688, 39680, 104192, 267264, 672256, 1662976, 4055040, 9764864, 23257088, 54853632, 128253952, 297533440, 685375488, 1568669696, 3569352704, 8078229504, 18192793600, 40785412096, 91049951232

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Formula

a(n) = 2^(n-3)*(n^3+9n^2+18n+8).

a(n) = Sum_{k=0..n} C(n, k)*(1+k)^3.

O.g.f.: (x-1)*(2*x^2-2*x-1)/(-1+2*x)^4. - R. J. Mathar, Apr 02 2008

a(n) = A058649(n+1)/n. [Gary Detlefs, Nov 26 2011]

Mathematica

LinearRecurrence[{8, -24, 32, -16}, {1, 9, 44, 170}, 30] (* Harvey P. Dale, Jul 30 2023 *)

Prog

(PARI) a(n) = sum(k=0, n, binomial(n, k)*(1+k)^3); \\ Michel Marcus, Oct 13 2016

Crossrefs

Cf. A000578, A058645.

Sequence in context: A229404 A059825 A074631 * A349878 A034558 A144109

Adjacent sequences: A084900 A084901 A084902 * A084904 A084905 A084906

Keyword

easy,nonn

Author

Paul Barry, Jun 13 2003

Status

approved