A024536 [ (4th elementary symmetric function of P(n))/(3rd elementary symmetric function of P(n)) ], where P(n) = {1, p(1), p(2), ..., p(n-1)}, p(0) = 1.

0, 1, 2, 4, 7, 10, 14, 19, 25, 32, 40, 49, 59, 70, 82, 95, 110, 125, 141, 159, 178, 197, 219, 242, 265, 290, 315, 341, 370, 400, 432, 464, 498, 534, 570, 608, 647, 688, 730, 773, 818, 863, 910, 957, 1007, 1060, 1114, 1168, 1224, 1281, 1338, 1398

Offset

4,3

Comments

p(i) denotes the i-th prime and [...] the floor function. - M. F. Hasler, Dec 11 2007

Links

Table of n, a(n) for n=4..55.

Formula

a(n) = floor(A024524(n)/A024523(n))

Prog

(PARI) /* symmetric polynomial of order n in X=[X1, ..., XN] */ sympol(X, n, s)=forvec(i=vector(n, j, [1, #X]), s+=prod(k=1, n, X[i[k]]), 2); s /* list of primes 0...n-1 with p(0)=1 */ P(n)=concat([1], vector(n-1, i, prime(i))) /* this sequence */ A024536(n) = sympol(P(n), 4) \ sympol(P(n), 3) \\ M. F. Hasler, Dec 11 2007

Crossrefs

Cf. A024523, A024524.

Sequence in context: A025710 A023536 A196126 * A177237 A094281 A076101

Adjacent sequences: A024533 A024534 A024535 * A024537 A024538 A024539

Keyword

nonn

Author

Clark Kimberling

Extensions

Extended (up to a(55)) by M. F. Hasler, Dec 11 2007

Status

approved