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

1,2

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).

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

Maple

f:=n->add((2*i+1)^6, i=0..n);
[seq(f(n), n=0..40)];

Prog

(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
(PARI) a(n) = n*(192*n^6-336*n^4+196*n^2-31)/21 \\ Charles R Greathouse IV, Jun 29 2015

Crossrefs

Cf. A000447, A002309, A016758.

Sequence in context: A158397 A031732 A224437 * A085441 A098292 A031525

Adjacent sequences: A259319 A259320 A259321 * A259323 A259324 A259325

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 24 2015

Status

approved