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A133708 First differences of A047835. 4
0, 0, 1, 69, 1694, 22932, 208152, 1413720, 7697052, 35194302, 139687119, 493127635, 1577331756, 4637757488, 12679063488, 32529562560, 78917794128, 182184724908, 402332471541, 853769650041, 1747606106554, 3462012537060, 6656436729800, 12452933493000 (list; graph; refs; listen; history; text; internal format)
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: A264283 A333034 A200826 * A253334 A017785 A017732

Adjacent sequences:  A133705 A133706 A133707 * A133709 A133710 A133711

KEYWORD

nonn

AUTHOR

Peter Bala, Sep 21 2007

STATUS

approved

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Last modified May 7 19:23 EDT 2021. Contains 343652 sequences. (Running on oeis4.)