|
| |
|
|
A104376
|
|
a(n) = Sum_{j=0..13} n^j.
|
|
8
|
|
|
|
1, 14, 16383, 2391484, 89478485, 1525878906, 15672832819, 113037178808, 628292358729, 2859599056870, 11111111111111, 37974983358324, 116719860413533, 328114698808274, 854769755812155, 2085209001813616, 4803839602528529, 10523614159962558, 22047845151887119
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,14,-1).
|
|
|
FORMULA
|
a(n) = n^13 + n^12 + n^11 + n^10 + n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n^1 + 1.
G.f.: (5461*x^12 + 1119288*x^11 + 37443654*x^10 + 372458048*x^9 + 1409085783*x^8 + 2263446576*x^7 + 1598944452*x^6 + 484853760*x^5 + 57484467*x^4 + 2163032*x^3 + 16278*x^2 + 1)/(1-x)^14. - Colin Barker, Nov 04 2012
|
|
|
MATHEMATICA
|
Table[1+Sum[n^j, {j, 1, 13}], {n, 0, 20}] (* G. C. Greubel, Apr 14 2019 *)
LinearRecurrence[{14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1}, {1, 14, 16383, 2391484, 89478485, 1525878906, 15672832819, 113037178808, 628292358729, 2859599056870, 11111111111111, 37974983358324, 116719860413533, 328114698808274}, 20] (* Harvey P. Dale, Sep 04 2023 *)
|
|
|
PROG
|
(Sage) [sum(n^j for j in (0..13)) for n in (0..20)] # G. C. Greubel, Apr 14 2019
|
|
|
CROSSREFS
|
Cf. similar sequences of the type a(n) = Sum_{j=0..m} n^j are: A000027 (m=1), A002061 (m=2), A053698 (m=3), A053699 (m=4), A053700 (m=5), A053716 (m=6), A053717 (m=7), A102909 (m=8), A103623 (m=9), A060885 (m=10), A105067 (m=11), A060887 (m=12), this sequence (m=13), A104682 (m=14), A105312 (m=15), A269442 (m=16), A269446 (m=18).
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Douglas Winston (douglas.winston(AT)srupc.com), Apr 16 2005
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
