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A103915
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Column k=10 sequence of array A103728.
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1
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1, 61, 7537, 41455, 618531, 12670589, 29075821, 247316941, 826985881, 1437223369, 3989619561, 15521533197, 51295084349, 74158059901, 207831585787, 391117136551, 528866563321, 1242387913729, 2113505780927, 4462952476841
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The two a(n) formulae, given below, produce natural numbers for all n>=0.
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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!.
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CROSSREFS
| For columns k=0..9 see A000012 (powers of 1), A040976 (primes p(n)-2), A103729-A103735, A103914.
Sequence in context: A181636 A167736 A015288 * A090823 A093261 A062638
Adjacent sequences: A103912 A103913 A103914 * A103916 A103917 A103918
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Feb 24 2005
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