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A103915 Column k=10 sequence of array A103728. 1
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; text; internal format)
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

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Last modified December 3 06:42 EST 2016. Contains 278698 sequences.