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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 (list; graph; refs; listen; history; text; internal format)
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]

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 * A034558 A144109 A099867

Adjacent sequences:  A084900 A084901 A084902 * A084904 A084905 A084906

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 13 2003

STATUS

approved

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Last modified May 16 14:39 EDT 2021. Contains 343949 sequences. (Running on oeis4.)