A103733 Column k=6 sequence of array A103728.

1, 191, 853, 7537, 17587, 71369, 363749, 574621, 1895149, 3744761, 5123791, 9167525, 19974397, 39789335, 49243141, 89502667, 129269281, 154098649, 253600309, 345942995, 535842121, 917491105, 1180249901, 1333475377

Offset: 0

Author

Wolfdieter Lang, Feb 24 2005

Keywords

• nonn
• easy

Comments

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

Crossrefs

Cf. A000040, A103718, A103728.

Formula

a(n) = A103728(n+4, 6) = (1 +(p(n+4)-1)*binomial(p(n+4)-1, 6))/p(n+4), with p(n) := A000040(n) (n-th prime).

a(n) = (2484 - 3388*p(n+4) + 2359*p(n+4)^2 - 910*p(n+4)^3 + 196*p(n+4)^4 - 22*p(n+4)^5 + p(n+4)^6)/6! = (Sum_{m=0..6} A103718(k, m)*p(n+4)^m)/6!.