|
Search: id:A103915
|
|
| |
|
| 1, 61, 7537, 41455, 618531, 12670589, 29075821, 247316941, 826985881, 1437223369, 3989619561, 15521533197, 51295084349, 74158059901, 207831585787, 391117136551, 528866563321, 1242387913729, 2113505780927, 4462952476841
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
The two a(n) formulae, given below, produce natural numbers for all n>=0.
|
|
FORMULA
|
a(n)=A103728(n+5, 10)=(1 +(p(n+5)-1)*binomial(p(n+5)-1, 10))/p(n+5), with p(n):=A000040(n) (n-th prime).
a(n)= (14257440 - 23382216*p(n+5) + 21163076*p(n+5)^2 - 11826430*p(n+5)^3 + 4318985*p(n+5)^4 - 1059828*p(n+5)^5 + 175923*p(n+5)^6 -19470*p(n+5)^7 + 1375*p(n+5)^8 - 56*p(n+5)^9 + 1*p(n+5)^10)/10! = sum(A103718(k, m)*p(n+5)^m, m=0..10)/10!.
|
|
CROSSREFS
|
For columns k=0..9 see A000012 (powers of 1), A040976 (primes p(n)-2), A103729-A103735, A103914.
Sequence in context: A126434 A096544 A015288 this_sequence A090823 A093261 A062638
Adjacent sequences: A103912 A103913 A103914 this_sequence A103916 A103917 A103918
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 24 2005
|
|
|
Search completed in 0.002 seconds
|
