A259322 Sum of sixth powers of odd numbers.
1, 730, 16355, 134004, 665445, 2437006, 7263815, 18654440, 42792009, 89837890, 175604011, 323639900, 567780525, 955201014, 1550024335, 2437528016, 3728995985, 5567261610, 8132988019, 11651731780, 16401836021, 22723199070, 31026964695
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- J. L. Bailey, Jr., A table to facilitate the fitting of certain logistic curves, Annals Math. Stat., 2 (1931), 355-359.
- J. L. Bailey, A table to facilitate the fitting of certain logistic curves, Annals Math. Stat., 2 (1931), 355-359. [Annotated scanned copy]
- F. E. Croxton and D. J. Cowden, Applied General Statistics, 2nd Ed., Prentice-Hall, Englewood Cliffs, NJ, 1955 [Annotated scans of just pages 742-743]
- Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
Programs
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Maple
f:=n->add((2*i+1)^6,i=0..n); [seq(f(n),n=0..40)];
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PARI
Vec(x*(x^6+722*x^5+10543*x^4+23548*x^3+10543*x^2+722*x+1)/(x-1)^8 + O(x^100)) \\ Colin Barker, Jun 29 2015
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PARI
a(n) = n*(192*n^6-336*n^4+196*n^2-31)/21 \\ Charles R Greathouse IV, Jun 29 2015
Formula
a(n) = (n*(-31+196*n^2-336*n^4+192*n^6))/21. - Colin Barker, Jun 29 2015
G.f.: x*(x^6+722*x^5+10543*x^4+23548*x^3+10543*x^2+722*x+1) / (x-1)^8. - Colin Barker, Jun 29 2015