|
|
A008454
|
|
Tenth powers: a(n) = n^10.
|
|
38
|
|
|
0, 1, 1024, 59049, 1048576, 9765625, 60466176, 282475249, 1073741824, 3486784401, 10000000000, 25937424601, 61917364224, 137858491849, 289254654976, 576650390625, 1099511627776, 2015993900449, 3570467226624, 6131066257801, 10240000000000, 16679880978201, 26559922791424
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Totally multiplicative sequence with a(p) = p^10 for prime p. [Jaroslav Krizek, Nov 01 2009]
Fifth powers of the squares and the squares of fifth powers. - Wesley Ivan Hurt, Apr 01 2016
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1).
|
|
FORMULA
|
Totally multiplicative sequence with a(p) = p^10 for primes p. [Jaroslav Krizek, Nov 01 2009]
G.f.: x*(x+1)*(x^8+1012*x^7+46828*x^6+408364*x^5+901990*x^4 +408364*x^3+46828*x^2+1012*x+1)/(1-x)^11.
E.g.f.: x*exp(x)*(x^9+45*x^8+750*x^7+5880*x^6+22827*x^5+42525*x^4+34105*x^3+9330*x^2+511*x+1). (End)
Sum_{n>=1} 1/a(n) = zeta(10) = Pi^10/93555 (A013668).
Sum_{n>=1} (-1)^(n+1)/a(n) = 511*zeta(10)/512 = 73*Pi^10/6842880. (End)
|
|
MAPLE
|
|
|
MATHEMATICA
|
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|