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A254647 Fourth partial sums of eighth powers (A001016). 15
1, 260, 7595, 94360, 723534, 4037712, 17944290, 67127880, 219319815, 642251428, 1718012933, 4258676240, 9892043980, 21721707840, 45414150132, 90930820464, 175208925885, 326205634020, 588861675535, 1033717781096, 1769137540730, 2958360418000, 4842936861750, 7774492635000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
G.f.: x*(1 +247*x +4293*x^2 +15619*x^3 +15619*x^4 +4293*x^5 +247*x^6 +x^7)/(1-x)^13.
a(n) = n*(1+n)*(2+n)^2*(3+n)*(4+n)*(1 +4*n +n^2)*(21 -48*n +20*n^2 + 16*n^3 +2*n^4)/23760.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + n^8.
EXAMPLE
The eighth powers: 1, 256, 6561, 65536, 390625, ... (A001016)
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, ... (A254642)
Fourth partial sums: 1, 260, 7595, 94360, 723534, ... (this sequence)
MAPLE
seq(binomial(n+4, 5)*(n+2)*((n+2)^2-3)*(2*(n+2)^4 -28*(n+2)^2 +101)/198, n=1..30); # G. C. Greubel, Aug 28 2019
MATHEMATICA
Table[n(1+n)(2+n)^2(3+n)(4+n)(1+4n+n^2)(21 -48n +20n^2 +16n^3 +2n^4 )/23760, {n, 20}] (* or *)
Accumulate[Accumulate[Accumulate[Accumulate[Range[20]^8]]]] (* or *)
CoefficientList[Series[(1 +247x +4293x^2 +15619x^3 +15619x^4 +4293x^5 + 247x^6 +x^7)/(1-x)^13, {x, 0, 19}], x]
PROG
(PARI) a(n)=n*(1+n)*(2+n)^2*(3+n)*(4+n)*(1+4*n+n^2)*(21-48*n+20*n^2 +16*n^3+2*n^4)/23760 \\ Charles R Greathouse IV, Sep 08 2015
(PARI) vector(30, n, m=n+2; binomial(m+2, 5)*m*(m^2-3)*(2*m^4-28*m^2 +101)/198)
(Magma) [Binomial(n+4, 5)*(n+2)*((n+2)^2-3)*(2*(n+2)^4 -28*(n+2)^2 +101)/198: n in [1..30]]; // G. C. Greubel, Aug 28 2019
(Sage) [binomial(n+4, 5)*(n+2)*((n+2)^2-3)*(2*(n+2)^4 -28*(n+2)^2 +101)/198 for n in (1..30)] # G. C. Greubel, Aug 28 2019
(GAP) List([1..30], n-> Binomial(n+4, 5)*(n+2)*((n+2)^2-3)*(2*(n+2)^4 -28*(n+2)^2 +101)/198); # G. C. Greubel, Aug 28 2019
CROSSREFS
Sequence in context: A287923 A238029 A264254 * A168187 A067639 A264162
KEYWORD
nonn,easy
AUTHOR
Luciano Ancora, Feb 05 2015
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)