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
Links
- Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).
Programs
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Mathematica
LinearRecurrence[{8,-24,32,-16},{1,9,44,170},30] (* Harvey P. Dale, Jul 30 2023 *) -
PARI
a(n) = sum(k=0, n, binomial(n, k)*(1+k)^3); \\ Michel Marcus, Oct 13 2016
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]