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A255177
Second differences of seventh powers (A001015).
7
1, 126, 1932, 12138, 47544, 140070, 341796, 730002, 1412208, 2531214, 4270140, 6857466, 10572072, 15748278, 22780884, 32130210, 44327136, 59978142, 79770348, 104476554, 134960280, 172180806, 217198212, 271178418
OFFSET
0,2
FORMULA
G.f.: (1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/(1 - x)^6.
a(n) = 14*n*(3*n^4 + 5*n^2 + 1) for n>0, a(0)=1.
a(n) = A022523(n)-A022523(n-1). - R. J. Mathar, Jul 16 2015
EXAMPLE
Second differences: 1, 126, 1932, 12138, 47544, ... (this sequence)
First differences: 1, 127, 2060, 14324, 63801, ... (A152726)
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The seventh powers: 1, 128, 2187, 16384, 78125, ... (A001015)
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First partial sums: 1, 129, 2316, 18700, 96825, ... (A000541)
Second partial sums: 1, 130, 2446, 21146, 117971, ... (A250212)
Third partial sums: 1, 131, 2577, 23723, 141694, ... (A254641)
Fourth partial sums: 1, 132, 2709, 26432, 168126, ... (A254646)
Fifth partial sums: 1, 133, 2842, 29274, 197400, ... (A254684)
MATHEMATICA
Join[{1}, Table[14 n (3 n^4 + 5 n^2 + 1), {n, 1, 30}], {n, 0, 24}] (* or *)
CoefficientList[Series[(1 + 120 x + 1191 x^2 + 2416 x^3 + 1191 x^4 + 120 x^5 + x^6)/(1 - x)^6, {x, 0, 22}], x]
PROG
(Magma) [1] cat [14*(-1+n)*(9-22*n+23*n^2-12*n^3+3*n^4): n in [2..30]]; // Vincenzo Librandi, Mar 12 2015
(Python)
def A255177(n): return 14*n*(n**2*(3*n**2 + 5) + 1) if n else 1 # Chai Wah Wu, Oct 07 2024
KEYWORD
nonn,easy,changed
AUTHOR
Luciano Ancora, Feb 21 2015
EXTENSIONS
Edited by Bruno Berselli, Mar 19 2015
STATUS
approved