OFFSET
1,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
FORMULA
a(1)=1; a(n)=sum(i^s, {i, n(n-1)/2+1, n(n-1)/2+1+n}).
a(n)=(3n^15 + 42n^13 + 168n^11 + 206n^9 - 11n^7 - 56n^5 + 32n^3)/384.
G.f.: x*(x^14 +2299*x^13 +337525*x^12 +11989784*x^11 +154720571*x^10 +875467853*x^9 +2397170367*x^8 +3336829200*x^7 +2397170367*x^6 +875467853*x^5 +154720571*x^4 +11989784*x^3 +337525*x^2 +2299*x +1)/(x-1)^16. [Colin Barker, Jul 22 2012]
EXAMPLE
s=7; a(1) = 1^s = 1; a(2) = 2^s + 3^s = 2^7 + 3^7 = 2315; a(3) = 4^s + 5^s + 6^s = 374445, a(4) = 7^s + 8^s + 9^s + 10^3 = 17703664.
MATHEMATICA
i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=7; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Sep 24 2002
EXTENSIONS
Formula from Charles R Greathouse IV, Sep 17 2009
STATUS
approved