A010822 Expansion of Product_{k>=1} (1 - x^k)^15.

1, -15, 90, -245, 105, 1107, -2485, 195, 4860, -2420, -3990, -8190, 19695, 13755, -38475, 3990, -9750, 34020, 43015, -46605, -13860, -127385, 106485, 165240, -79275, -16380, -92340, -35840, -151995, 188550, 315783, 90090, -271215, -307485, 20475, -505440, 915385, 209340, -284130, 337645, -294225, 269325, -1707970, -70305, 1297620, 574210, 492765, 251370, -847245, -1102725, 438129, -1416190, 641445, 0

Offset

0,2

References

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

Van der Blij, F. "The function tau(n) of S. Ramanujan (an expository lecture)." Math. Student 18 (1950): 83-99. See page 85.

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

Formula

a(0) = 1, a(n) = -(15/n)*Sum_{k=1..n} A000203(k)*a(n-k) for n > 0. - Seiichi Manyama, Mar 27 2017

G.f.: exp(-15*Sum_{k>=1} x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Feb 05 2018

Example

1 - 15*x + 90*x^2 - 245*x^3 + 105*x^4 + 1107*x^5 - 2485*x^6 + 195*x^7 + ...

Mathematica

a[0] = 1; a[n_] := a[n] = -15/n Sum[DivisorSigma[1, k] a[n-k], {k, 1, n}];
Table[a[n], {n, 0, 53}] (* Jean-François Alcover, Dec 19 2018, after Seiichi Manyama *)

Crossrefs

See A322043 for the coefficients that are zero.

Cf. also A000594.

Sequence in context: A220150 A164541 A145789 * A316224 A022707 A323334

Adjacent sequences: A010819 A010820 A010821 * A010823 A010824 A010825

Keyword

sign

Author

N. J. A. Sloane.

Status

approved