|
|
A254144
|
|
a(n) = 1*6^n + 2*5^n + 3*4^n + 4*3^n + 5*2^n + 6*1^n.
|
|
7
|
|
|
21, 56, 196, 812, 3724, 18236, 93436, 494732, 2685004, 14851676, 83384476, 473755052, 2717541484, 15709845116, 91395715516, 534498925772, 3139343105164, 18504595174556, 109397060622556, 648335998054892, 3850205790608044
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
This is the sequence of sixth terms of "second partial sums of m-th powers".
|
|
LINKS
|
|
|
FORMULA
|
G.f.: -(8028*x^5 - 13916*x^4 + 8939*x^3 - 2695*x^2 + 385*x - 21) / ((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)). - Colin Barker, Jan 26 2015
a(n) = (x + 1)*( Bernoulli(n + 1, x + 1) - Bernoulli(n + 1, 1) )/(n + 1) - ( Bernoulli(n + 2, x + 1) - Bernoulli(n + 2, 1) )/(n + 2) at x = 6.
a(n) = (1/5!)*Sum_{k = 0..n} (-1)^(k+n)*(k + 7)!*Stirling2(n,k)/ ((k + 1)*(k + 2)). (End)
|
|
MAPLE
|
seq(add(i*(7 - i)^n, i = 1..6), n = 0..20); # Peter Bala, Jan 31 2017
|
|
MATHEMATICA
|
Table[5 2^n + 3 4^n + 4 3^n + 2 5^n + 6^n + 6, {n, 0, 25}] (* Bruno Berselli, Jan 27 2015 *)
|
|
PROG
|
(PARI) Vec(-(8028*x^5-13916*x^4+8939*x^3-2695*x^2+385*x-21)/((x-1)*(2*x-1)*(3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)) + O(x^100)) \\ Colin Barker, Jan 26 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|