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Revision History for A000542 (Bold, blue-underlined text is an addition; faded, red-underlined text is a deletion.)

Showing entries 1-10 | older changes
Sum of 8th powers: 1^8 + 2^8 + ... + n^8.
(history; published version)
#68 by Alois P. Heinz at Mon May 27 12:26:22 EDT 2024
STATUS

proposed

approved

#67 by Michel Marcus at Mon May 27 12:13:09 EDT 2024
STATUS

editing

proposed

#66 by Michel Marcus at Sun May 26 23:56:32 EDT 2024
LINKS

B. Bruno Berselli, A description of the recursive method in Comments lines: website <a href="http://www.lanostra-matematica.org/2008/12/sequenze-numeriche-e-procedimenti.html">Matem@ticamente</a> (in Italian).

FORMULA

a(n) = -Sum_{j=1..8} j*sStirling1(n+1,n+1-j)*SStirling2(n+8-j,n), where s(n,k) and S(n,k) are the Stirling numbers of the first kind and the second kind, respectively. - Mircea Merca, Jan 25 2014

STATUS

approved

editing

#65 by Ray Chandler at Wed Jun 28 20:25:37 EDT 2023
STATUS

editing

approved

#64 by Ray Chandler at Wed Jun 28 20:25:26 EDT 2023
FORMULA

G.f.: x*(x+1)*(x^6 + 246*x^5 + 4047*x^4 + 11572*x^3 + 4047*x^2 + 246*x + 1)/(x-1)^10). - Colin Barker, May 27 2012

STATUS

approved

editing

#63 by Jon E. Schoenfield at Sun Dec 19 09:36:51 EST 2021
STATUS

editing

approved

#62 by Jon E. Schoenfield at Sun Dec 19 09:36:48 EST 2021
FORMULA

a(n) = n*(n+1)*(2*n+1)*(5*n^6 + 15*n^5 + 5*n^4 - 15*n^3 - n^2 + 9*n - 3)/90.

a(n) = n*A000541(n) - sum(Sum_{i=0..n-1} A000541(i), i=0..n-1). - Bruno Berselli, Apr 26 2010

G.f.: x*(x+1)*(x^6 + 246*x^5 + 4047*x^4 + 11572*x^3 + 4047*x^2 + 246*x + 1)/(x-1)^10). - Colin Barker, May 27 2012

a(n) = -sum(Sum_{j=1..8, } j*s(n+1,n+1-j)*S(n+8-j,n)), , where s(n,k) and S(n,k) are the Stirling numbers of the first kind and the second kind, respectively. - Mircea Merca, Jan 25 2014

PROG

(Sage) [bernoulli_polynomial(n, 9)/9 for n in range(1, 25)] # - __Zerinvary Lajos_, May 17 2009

AUTHOR
STATUS

approved

editing

#61 by Peter Luschny at Sat Apr 11 06:34:18 EDT 2020
STATUS

editing

approved

#60 by Peter Luschny at Sat Apr 11 06:34:10 EDT 2020
PROG

for _ in range(10**224):

A000542_list.append(m[-1]) # _Chai Wah Wu_, Nov 05 2014

print(A000542_list) # Chai Wah Wu, Nov 05 2014

STATUS

proposed

editing

#59 by F. Chapoton at Sat Apr 11 05:19:12 EDT 2020
STATUS

editing

proposed