login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A254684 Fifth partial sums of seventh powers (A001015). 6
1, 133, 2842, 29274, 197400, 1001952, 4137966, 14597934, 45454773, 127861825, 330540028, 795609724, 1801339176, 3867558072, 7926516900, 15591322404, 29566276257, 54259095093, 96674782246, 167695627750, 283882296880 (list; graph; refs; listen; history; text; internal format)
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

Luciano Ancora, Pascal’s triangle and recurrence relations  for partial sums of m-th powers

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 - 120*x^2 - 1191*x^3 - 2416*x^4 - 1191*x^5 - 120*x^6 - x^7)/(- 1 + x)^13.

a(n) = n*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*(-3 + 5*n + n^2)*(-2 + 5*n + n^2)*(5 + 5*n + n^2)/95040.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) + n^7.

EXAMPLE

First differences:   1, 127, 2060, 14324,  63801, ...  (A152726)

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

The seventh powers:  1, 128, 2187, 16384,  78125, ...  (A001015)

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

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, ...  (this sequence)

MATHEMATICA

Table[n (1 + n) (2 + n) (3 + n) (4 + n) (5 + n) (- 3 + 5 n + n^2) (- 2 + 5 n + n^2) (5 + 5 n + n^2)/95040, {n, 21}] (* or *)

CoefficientList[Series[(- 1 - 120 x - 1191 x^2 - 2416 x^3 - 1191 x^4 - 120 x^5 - x^6)/(-1 + x)^13, {x, 0, 20}], x]

PROG

(PARI) a(n)=n*(1+n)*(2+n)*(3+n)*(4+n)*(5+n)*(-3+5*n+n^2)*(-2+5*n+n^2)*(5+5*n+n^2)/95040 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A000541, A001015, A152726, A250212, A254641, A254646, A254681, A254682, A254683.

Sequence in context: A020265 A028295 A262121 * A133240 A129050 A129049

Adjacent sequences:  A254681 A254682 A254683 * A254685 A254686 A254687

KEYWORD

nonn,easy

AUTHOR

Luciano Ancora, Feb 12 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 10 04:38 EDT 2020. Contains 336368 sequences. (Running on oeis4.)