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A084903
Binomial transform of positive cubes.
1
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
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
Sequence in context: A229404 A059825 A074631 * A349878 A034558 A144109
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jun 13 2003
STATUS
approved