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