

A061166


Polynomial extrapolation of 2, 3, 5, 7, 11, 13, 17.


1



2, 3, 5, 7, 11, 13, 17, 72, 332, 1139, 3129, 7361, 15469, 29837, 53797, 91850, 149910, 235571, 358397, 530235, 765551, 1081789, 1499753, 2044012, 2743328, 3631107, 4745873, 6131765, 7839057, 9924701, 12452893, 15495662, 19133482, 23455907
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OFFSET

1,1


LINKS



FORMULA

a(n) = (23n^6537n^5+4925n^422515n^3+53732n^261548n+27360)/720.
G.f.: x*(211*x+26*x^235*x^3+32*x^429*x^5+38*x^6)/(1x)^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 (211x+26x^235x^3+32x^429x^5+38x^6)/(1x)^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



STATUS

approved



