A103915 Column k=10 sequence of array A103728.

1, 61, 7537, 41455, 618531, 12670589, 29075821, 247316941, 826985881, 1437223369, 3989619561, 15521533197, 51295084349, 74158059901, 207831585787, 391117136551, 528866563321, 1242387913729, 2113505780927, 4462952476841

Offset

0,2

Comments

The two a(n) formulas, given below, produce natural numbers for all n>=0.

Links

Table of n, a(n) for n=0..19.

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: A015288 A219113 A210686 * A090823 A093261 A062638

Adjacent sequences: A103912 A103913 A103914 * A103916 A103917 A103918

Keyword

nonn,easy

Author

Wolfdieter Lang, Feb 24 2005

Status

approved