A291489 -id:A291489 - cp's OEIS frontend

A291645 Expansion of the series reversion of -1 + Product_{k>=1} (1 + x^(k^2)).

1, 0, 0, -1, -1, 0, 4, 9, 4, -23, -78, -78, 132, 694, 1088, -443, -6169, -13452, -4646, 52247, 155891, 143796, -391672, -1715015, -2481013, 2107735, 17836000, 35704800, 3037215, -172386166, -465009936, -338007604, 1487272659, 5624864403, 7125599375, -10208041482

Offset: 1

Ilya Gutkovskiy, Aug 28 2017

sign

Reversion of g.f. (with constant term omitted) for A033461.

N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Series Reversion
Index entries for reversions of series

Cf. A007312, A033461, A050393, A291489.

nmax = 36; Rest[CoefficientList[InverseSeries[Series[-1 + Product[1 + x^k^2, {k, 1, nmax}], {x, 0, nmax}], x], x]]

G.f. A(x) satisfies: -1 + Product_{k>=1} (1 + A(x)^(k^2)) = x.

A291646 Expansion of the series reversion of -1 + Product_{k>=1} (1 + x^(2*k-1)).

Original entry on oeis.org

1, 0, -1, -1, 2, 6, -1, -29, -32, 108, 311, -185, -1991, -1590, 9468, 22163, -26645, -170511, -70359, 955734, 1755790, -3561052, -16020532, 309754, 102695477, 141637053, -463468990, -1567907433, 806541136, 11367276801, 10768399120, -59447130815, -155142592628, 172852194214, 1273466836673

Offset: 1

Ilya Gutkovskiy, Aug 28 2017

sign

Reversion of g.f. (with constant term omitted) for A000700.

N. J. A. Sloane, Transforms
Eric Weisstein's World of Mathematics, Series Reversion
Index entries for reversions of series

Cf. A000700, A007312, A050393, A291489.

nmax = 35; Rest[CoefficientList[InverseSeries[Series[-1 + Product[1 + x^(2 k - 1), {k, 1, nmax}], {x, 0, nmax}], x], x]]
nmax = 35; Rest[CoefficientList[InverseSeries[Series[-1 + QPochhammer[x^2]^2/(QPochhammer[x] QPochhammer[x^4]), {x, 0, nmax}], x], x]]

G.f. A(x) satisfies: -1 + Product_{k>=1} (1 + A(x)^(2*k-1)) = x.

cp's OEIS Frontend

A291645 Expansion of the series reversion of -1 + Product_{k>=1} (1 + x^(k^2)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula