OFFSET
1,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).
FORMULA
a(n) = (23n^6-537n^5+4925n^4-22515n^3+53732n^2-61548n+27360)/720.
G.f.: x*(2-11*x+26*x^2-35*x^3+32*x^4-29*x^5+38*x^6)/(1-x)^7. [Colin Barker, Mar 28 2012]
EXAMPLE
a(8)=72 since first differences of (2,3,5,7,11,13,17) are (1,2,2,4,2,4), second differences (1,0,2,-2,2), third differences (-1,2,-4,4), fourth differences (3,-6,8), fifth differences (-9,14) and sixth differences (23) so a(8)=17+4+2+4+8+14+23=72.
MATHEMATICA
CoefficientList[Series[x (2-11x+26x^2-35x^3+32x^4-29x^5+38x^6)/(1-x)^7, {x, 0, 50}], x] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {2, 3, 5, 7, 11, 13, 17}, 50] (* Harvey P. Dale, Aug 14 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Apr 18 2001
STATUS
approved