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A166869 a(n) = n * A056219(n+1). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

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)*b[n]: n in [2..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)*b[n] for n in (2..max)] # G. C. Greubel, Nov 29 2019

CROSSREFS

Cf. A056219, A166870.

Sequence in context: A290440 A090922 A056228 * A168380 A335730 A308286

Adjacent sequences:  A166866 A166867 A166868 * A166870 A166871 A166872

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Oct 22 2009

STATUS

approved

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Last modified July 6 03:46 EDT 2020. Contains 335475 sequences. (Running on oeis4.)