A133708 First differences of A047835.

0, 0, 1, 69, 1694, 22932, 208152, 1413720, 7697052, 35194302, 139687119, 493127635, 1577331756, 4637757488, 12679063488, 32529562560, 78917794128, 182184724908, 402332471541, 853769650041, 1747606106554, 3462012537060, 6656436729800, 12452933493000

Offset

1,4

Links

T. D. Noe, Table of n, a(n) for n = 1..1003

Formula

In terms of Vandermonde determinants, a(n) = 1/864*sum {1 <= x_1,x_2,x_3 <= n} (x_1*x_2*x_3)^2*(det V(x_1,x_2,x_3))^2 = 1/864 *sum {1 <= i,j,k <= n} (i*j*k*(i-j)(i-k)(j-k))^2, where V(x_1,x_2,x_3) is the Vandermonde matrix of order 3. a(n) = (n-2)*(n-1)^2*n^3*(n+1)^3*(n+2)^2*(n+3)*(n^2+n+3)*(2n+1)/108864000.

Empirical G.f.: x^3*(x+1)*(x^8+52*x^7+658*x^6+2890*x^5+4810*x^4+2890*x^3+658*x^2+52*x+1)/(x-1)^16. [Colin Barker, Jun 06 2012]

Mathematica

Join[{0, 0, 1}, Differences[Table[Product[Times@@((i+Range[4, 7])/(i+Range[0, 3])), {i, n}], {n, 0, 30}]]] (* Harvey P. Dale, Aug 08 2015 *)

Crossrefs

Cf. A040977, A047819, A047835, A107915.

Sequence in context: A333034 A200826 A359105 * A253334 A017785 A017732

Adjacent sequences: A133705 A133706 A133707 * A133709 A133710 A133711

Keyword

nonn

Author

Peter Bala, Sep 21 2007

Status

approved