OFFSET
0,3
REFERENCES
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 815.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 155.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Bruno Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian).
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
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.
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) = 9*a(n-1) - 36* a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) + 40320. - Ant King, Sep 24 2013
a(n) = -Sum_{j=1..8} j*Stirling1(n+1,n+1-j)*Stirling2(n+8-j,n). - Mircea Merca, Jan 25 2014
MAPLE
a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+n^8 od: seq(a[n], n=0..23); # Zerinvary Lajos, Feb 22 2008
MATHEMATICA
lst={}; s=0; Do[s=s+n^8; AppendTo[lst, s], {n, 10^2}]; lst..or..Table[Sum[k^8, {k, 1, n}], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Aug 14 2008 *)
s = 0; lst = {s}; Do[s += n^8; AppendTo[lst, s], {n, 1, 30, 1}]; lst (* Zerinvary Lajos, Jul 12 2009 *)
Accumulate[Range[0, 30]^8] (* Harvey P. Dale, Jun 17 2015 *)
PROG
(Sage) [bernoulli_polynomial(n, 9)/9 for n in range(1, 25)] # Zerinvary Lajos, May 17 2009
(Python)
A000542_list, m = [0], [40320, -141120, 191520, -126000, 40824, -5796, 254, -1, 0, 0]
for _ in range(24):
for i in range(9):
m[i+1] += m[i]
A000542_list.append(m[-1])
print(A000542_list) # Chai Wah Wu, Nov 05 2014
(PARI) 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 \\ Charles R Greathouse IV, Sep 28 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved