A278407 G.f.: x^2 * f''(x), where f(x) = Product_{k>=1} (1 + x^k).

0, 0, 2, 12, 24, 60, 120, 210, 336, 576, 900, 1320, 1980, 2808, 4004, 5670, 7680, 10336, 14076, 18468, 24320, 31920, 41118, 52624, 67344, 85200, 107250, 134784, 167832, 207872, 257520, 316200, 386880, 473088, 574464, 696150, 841680, 1012320, 1214784, 1455324

Offset: 0

Author

Vaclav Kotesovec, Nov 21 2016

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000009, A066189, A278406.

Programs

Maple

g:= mul(1+x^k,k=1..100):
S1:= series(g,x,101):
S2:= series(x^2*diff(S1,x$2),x,101):
seq(coeff(S2,x,j),j=0..100); # Robert Israel, Nov 22 2016

Mathematica

nmax=60; CoefficientList[Series[x^2*D[Product[1+x^k, {k, 1, nmax}], {x, 2}], {x, 0, nmax}], x]
nmax=60; CoefficientList[Series[Product[1+x^k, {k, 1, nmax}], {x, 0, nmax}], x]*Range[0, nmax]*(Range[0, nmax]-1)

Formula

a(n) = n*(n-1)*A000009(n).