A103733 - OEIS

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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

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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..23.

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!.

CROSSREFS

Cf. A000040, A103718, A103728.

Sequence in context: A082445 A108848 A052165 * A217500 A142451 A083980

Adjacent sequences: A103730 A103731 A103732 * A103734 A103735 A103736

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Feb 24 2005

STATUS

approved