login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A253712 Second partial sums of 12th powers (A008456). 0
1, 4098, 539636, 17852390, 279305769, 2717541484, 18997064400, 103996064052, 471424600185, 1838853136318, 6344710049172, 19766667410282, 56486709893873, 149900664752760, 373060957502272, 877696226962440, 1964953733652369, 4209042621768474, 8666446428950740, 17219850236133006, 33129081554701913, 61893315504320036 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The formula for the second partial sums of m-th powers is: b(n,m) = (n+1)*F(m) - F(m+1), where F(m) are the m-th Faulhaber's formulas.

LINKS

Table of n, a(n) for n=1..22.

Luciano Ancora, Recurrence relation for the second partial sums of m-th powers

Luciano Ancora, Second partial sums of the m-th powers

FORMULA

a(n) = (n+1)^2*n*(n+2)*(30*n^10+300*n^9+925*n^8+200*n^7-3022*n^6-772*n^5+7073*n^4-1228*n^3-7888*n^2+5528*n-691)/5460.

a(n) = 2*a(n-1)-a(n-2)+n^12.

G.f.: x*(1 + 4083*x + 478271*x^2 + 10187685*x^3 + 66318474*x^4 + 162512286*x^5 + 162512286*x^6 + 66318474*x^7 + 10187685*x^8 + 478271*x^9 + 4083*x^10 + x^11)/(1-x)^15. - Vincenzo Librandi, Jan 19 2015

MATHEMATICA

RecurrenceTable[{a[n] == 2 a[n - 1] - a[n - 2] + n^12, a[1] == 1, a[2] == 4098}, a, {n, 1, 25}] (* Bruno Berselli, Jan 19 2015 *)

Table[(n + 1)^2 n (n + 2) (30 n^10 + 300 n^9 + 925 n^8 + 200 n^7 - 3022 n^6 - 772 n^5 + 7073 n^4 - 1228 n^3 - 7888 n^2 + 5528 n - 691)/5460, {n, 1, 25}] (* Vincenzo Librandi, Jan 19 2015 *)

PROG

(MAGMA) [(n+1)^2*n*(n+2)*(30*n^10+300*n^9+925*n^8+200*n^7-3022*n^6-772*n^5+7073*n^4-1228*n^3-7888*n^2+5528*n-691)/5460: n in [1..30]]; // Vincenzo Librandi, Jan 19 2015

CROSSREFS

Sequence in context: A226695 A031562 A282548 * A023354 A226694 A043476

Adjacent sequences:  A253709 A253710 A253711 * A253713 A253714 A253715

KEYWORD

nonn

AUTHOR

Luciano Ancora, Jan 12 2015

EXTENSIONS

a(22) corrected by Vincenzo Librandi, Jan 19 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 15 22:20 EST 2018. Contains 317252 sequences. (Running on oeis4.)