A010838 Expansion of Product_{k>=1} (1-x^k)^44.

1, -44, 902, -11352, 96965, -582692, 2428382, -6245448, 3684670, 43828180, -195750104, 340202584, 211248851, -2418539816, 4734800950, -43313600, -16560186918, 26632794760, 4021681554, -50231748600, 12519655368

Offset: 0

Author

N. J. A. Sloane

Keywords

• sign

References

• Newman, Morris; A table of the coefficients of the powers of eta(tau). Nederl. Akad. Wetensch. Proc. Ser. A. 59 = Indag. Math. 18 (1956), 204-216.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• M. Boylan, Exceptional congruences for the coefficients of certain eta-product newforms, J. Number Theory 98 (2003), no. 2, 377-389.
• Index entries for expansions of Product_{k >= 1} (1-x^k)^m

Crossrefs

Column k=44 of A286354.

Cf. A000203.

Programs

Mathematica

With[{nn=20},CoefficientList[Series[Product[(1-x^k)^44,{k,nn}],{x,0,nn}],x]] (* Harvey P. Dale, Mar 23 2015 *)

Formula

a(0) = 1, a(n) = -(44/n) * Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Aug 13 2023