OFFSET
1,2
LINKS
Luciano Ancora, Table of n, a(n) for n = 1..1000
Luciano Ancora, Partial sums of m-th powers with Faulhaber polynomials
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
FORMULA
G.f.: (x + 247*x^2 + 4293*x^3 + 15619*x^4 + 15619*x^5 + 4293*x^6 + 247*x^7 + x^8)/(- 1 + x)^12.
a(n) = n*(1 + n)*(2 + n)*(3 + n)*(3 + 2*n)*(1 + 36*n - 69*n^2 + 45*n^4 + 18*n^5 + 2*n^6)/3960.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + n^8.
EXAMPLE
First differences: 1, 255, 6305, 58975, 325089, ...(A022524)
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The eighth powers: 1, 256, 6561, 65536, 390625, ...(A001016)
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First partial sums: 1, 257, 6818, 72354, 462979, ...(A000542)
Second partial sums: 1, 258, 7076, 79430, 542409, ...(A253636)
Third partial sums: 1, 259, 7335, 86765, 629174, ...(this sequence)
MATHEMATICA
Table[n (1 + n) (2 + n) (3 + n) (3 + 2 n) (1 + 36 n - 69 n^2 + 45 n^4 + 18 n^5 + 2 n^6)/3960, {n, 22}]
Accumulate[Accumulate[Accumulate[Range[22]^8]]]
CoefficientList[Series[(1 + 247 x + 4293 x^2 + 15619 x^3 + 15619 x^4 + 4293 x^5 + 247 x^6 + x^7)/(- 1 + x)^12, {x, 0, 22}], x]
PROG
(PARI) a(n)=n*(1+n)*(2+n)*(3+n)*(3+2*n)*(1+36*n-69*n^2+45*n^4+18*n^5+2*n^6)/3960 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Feb 05 2015
STATUS
approved