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A255179 Second differences of ninth powers (A001017). 3
1, 510, 18660, 223290, 1448520, 6433590, 22151340, 63588210, 159338640, 359376750, 745368180, 1443884970, 2642886360, 4611828390, 7725765180, 12493804770, 19592282400, 29903014110, 44556993540, 64983894810, 92967744360, 130709124630, 180894272460 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Luciano Ancora, Table of n, a(n) for n = 0..1000

Luciano Ancora, Sums of powers of positive integers and their recurrence relations, section 0.5.

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

FORMULA

G.f.: (1 + 502*x + 14608*x^2 + 88234*x^3 + 156190*x^4 + 88234*x^5 + 14608*x^6 + 502*x^7 + x^8)/(1 - x)^8.

a(n) = 6*n*(3 + 28*n^2 + 42*n^4 + 12*n^6) for n>0, a(0)=1.

EXAMPLE

Second differences:  1, 510, 18660, 223290, 1448520, ... (this sequence)

First differences:   1, 511, 19171, 242461, 1690981, ... (A022525)

------------------------------------------------------------------------

The ninth powers:    1, 512, 19683, 262144, 1953125, ... (A001017)

------------------------------------------------------------------------

First partial sums:  1, 513, 20196, 282340, 2235465, ... (A007487)

Second partial sums: 1, 514, 20710, 303050, 2538515, ... (A253637)

Third partial sums:  1, 515, 21225, 324275, 2862790, ... (A254643)

MATHEMATICA

Join[{1}, Table[6 n (3 + 28 n^2 + 42 n^4 + 12 n^6), {n, 1, 30}]]

Join[{1}, Differences[Range[0, 30]^9, 2]] (8 or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {1, 510, 18660, 223290, 1448520, 6433590, 22151340, 63588210, 159338640}, 30] (* Harvey P. Dale, Jan 26 2019 *)

PROG

(MAGMA) [1] cat [6*n*(3+28*n^2+42*n^4+12*n^6): n in [1..30]]; // Vincenzo Librandi, Mar 12 2015

CROSSREFS

Cf. A001017, A007487, A022525, A253637, A254643, A255177, A255178.

Sequence in context: A252883 A196674 A260598 * A144768 A196289 A027494

Adjacent sequences:  A255176 A255177 A255178 * A255180 A255181 A255182

KEYWORD

nonn,easy

AUTHOR

Luciano Ancora, Feb 21 2015

EXTENSIONS

Corrected g.f. by Bruno Berselli, Feb 25 2015

Offset changed by Bruno Berselli, Mar 20 2015

STATUS

approved

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Last modified April 6 18:27 EDT 2020. Contains 333286 sequences. (Running on oeis4.)