A103735 -id:A103735 - cp's OEIS frontend

A103914 Negative of column k=9 sequence of array A103728.

9, 203, 10767, 46061, 475793, 6668731, 13845629, 91598867, 266769639, 435522233, 1078275557, 3609658883, 10468384561, 14540796059, 36461681717, 64117563369, 83947073543, 180056219381, 289521339853, 564930693271, 1283176845407

Offset: 0

Wolfdieter Lang, Feb 24 2005

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

Cf. A103735 (k=8).

a(n)=-A103728(n+5, 9)=-(1 -(p(n+5)-1)*binomial(p(n+5)-1, 9))/p(n+5), with p(n):=A000040(n) (n-th prime).

a(n)= -(1389456 - 2199276*p(n+5) + 1896380*p(n+5)^2 - 993005*p(n+5)^3 + 332598*p(n+5)^4 - 72723*p(n+5)^5 + 10320*p(n+5)^6 - 915*p(n+5)^7 + 46*p(n+5)^8 - p(n+5)^9)/9! = -sum(A103718(k, m)*p(n+5)^m, m=0..9)/9!.

A103915 Column k=10 sequence of array A103728.

Original entry on oeis.org

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

Offset: 0

Wolfdieter Lang, Feb 24 2005

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

For columns k=0..9 see A000012 (powers of 1), A040976 (primes p(n)-2), A103729-A103735, A103914.

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!.

cp's OEIS Frontend

A103914 Negative of column k=9 sequence of array A103728.

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