A001555 a(n) = 1^n + 2^n + ... + 8^n. (Formerly M4520 N1914)

8, 36, 204, 1296, 8772, 61776, 446964, 3297456, 24684612, 186884496, 1427557524, 10983260016, 84998999652, 660994932816, 5161010498484, 40433724284976, 317685943157892, 2502137235710736, 19748255868485844, 156142792528260336, 1236466399775623332

Offset

0,1

Comments

Conjectures for o.g.f.s for this type of sequence appear in the PhD thesis by Simon Plouffe. See A001552 for the reference. These conjectures are proved in a link given in A196837. [Wolfdieter Lang, Oct 15 2011]

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. 813.

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 and Robert Israel, Table of n, a(n) for n = 0..1000 (n = 0..200 from T. D. Noe)

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].

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 368

Formula

From Wolfdieter Lang, Oct 15 2011 (Start)

E.g.f.: (1-exp(8*x))/(exp(-x)-1) = Sum_{j=1..8} exp(j*x) (trivial).

O.g.f.: 4*(2-9*x)*(1-27*x+288*x^2-1539*x^3+4299*x^4-5886*x^5+3044*x^6) / Product_{j=1..8} (1-j*x). From the e.g.f. via Laplace transformation. See the proof in a link under A196837. (End)

a(n) = A001554(n) + A001018(n). - Michel Marcus, Jul 26 2013

Maple

seq(add(j^n, j=1..8), n=0..20); # Robert Israel, Aug 23 2015

Mathematica

Table[Total[Range[8]^n], {n, 0, 20}] (* T. D. Noe, Aug 09 2012 *)

Prog

(PARI) first(m)=vector(m, n, n--; sum(i=1, 8, i^n)) \\ Anders Hellström, Aug 23 2015

Crossrefs

Column 8 of array A103438.

Cf. A001018, A001552, A001554, A196837.

Sequence in context: A341543 A290357 A030112 * A032770 A032794 A000757

Adjacent sequences: A001552 A001553 A001554 * A001556 A001557 A001558

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Jon E. Schoenfield, Mar 24 2010

Status

approved