A166869 a(n) = n * A056219(n+1).

2, 4, 12, 20, 30, 54, 91, 120, 171, 250, 374, 504, 663, 854, 1170, 1568, 2074, 2628, 3325, 4180, 5313, 6754, 8602, 10656, 13100, 16042, 19683, 24024, 29464, 36000, 43834, 52768, 63228, 75582, 90510, 107856, 128575, 153178, 182208, 215400

Offset: 1

Author

Roger L. Bagula, Oct 22 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A056219, A166870.

Programs

Magma

max:=50;
R:=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)*b[n]: n in [2..max-1]]; // G. C. Greubel, Nov 29 2019

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*b[n+1], n=1..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, max}] (* G. C. Greubel, Nov 29 2019 *)

Sage

max=50;
def A056219_list(prec):
    P. = 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)*b[n] for n in (2..max)] # G. C. Greubel, Nov 29 2019