A166870 a(n) = n*(n-1)*A056219(n+1).

4, 24, 60, 120, 270, 546, 840, 1368, 2250, 3740, 5544, 7956, 11102, 16380, 23520, 33184, 44676, 59850, 79420, 106260, 141834, 189244, 245088, 314400, 401050, 511758, 648648, 824992, 1044000, 1315020, 1635808, 2023296, 2494206, 3077340

Offset

2,1

Links

G. C. Greubel, Table of n, a(n) for n = 2..1000

Maple

N:= 100; b:= seq(coeff(series(add(x^((1/2)*n*(n+1))*mul(x +1/(1-x^k), k=1..n), n = 1..floor((1/2)*sqrt(9+8*N))), x, N+2), x, j), j = 1..N+1); seq(n*(n-1)*b[n+1], n=2..N); # G. C. Greubel, Nov 29 2019

Mathematica

max:= 100; b:= CoefficientList[Series[Sum[x^(n*(n+1)/2)*Product[(x +1/(1-x^k)), {k, n}], {n, Floor[Sqrt[9 +8*(max+5)]/2]}], {x, 0, max+5}], x]; Table[n*b[[n + 2]], {n, 2, max}] (* G. C. Greubel, Nov 29 2019 *)

Prog

(Magma)
max:=50;
R<x>:=PowerSeriesRing(Integers(), max); b:= Coefficients(R!( (&+[x^Binomial(n+1, 2)*(&*[x + 1/(1-x^j): j in [1..n]]): n in [1..Floor(Sqrt(9+8*max)/2)]]) ));
[(n-1)*(n-2)*b[n]: n in [3..max-1]]; // G. C. Greubel, Nov 29 2019
(Sage)
max=50;
def A056219_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( sum(x^binomial(n+1, 2)*product((x + 1/(1-x^j)) for j in (1..n)) for n in (1..floor(sqrt(9+8*max)/2))) ).list()
b=A056219_list(max);
[(n-1)*(n-2)*b[n] for n in (3..max)] # G. C. Greubel, Nov 29 2019

Crossrefs

Cf. A056219, A166869.

Sequence in context: A157625 A128205 A085250 * A124350 A112611 A363092

Adjacent sequences: A166867 A166868 A166869 * A166871 A166872 A166873

Keyword

nonn,less

Author

Roger L. Bagula, Oct 22 2009

Status

approved