A307311 Expansion of Product_{k>=1} 1/(1 + x^k/(1 - x)^k).

1, -1, -1, -2, -3, -4, -5, -6, -6, -1, 19, 74, 200, 461, 977, 1987, 3976, 7902, 15559, 30105, 56778, 103833, 183765, 314882, 523007, 841752, 1305431, 1916607, 2540433, 2609983, 381628, -8814988, -36463325, -109113400, -285322360, -689608522, -1579574566, -3477967848

Offset

0,4

Comments

First differences of the binomial transform of A081362.

Convolution inverse of A129519.

Links

Robert Israel, Table of n, a(n) for n = 0..1000

Maple

a:=series(mul(1/(1+x^k/(1-x)^k), k=1..100), x=0, 38): seq(coeff(a, x, n), n=0..37); # Paolo P. Lava, Apr 02 2019

Mathematica

nmax = 40; CoefficientList[Series[Product[1/(1 + x^k/(1 - x)^k), {k, 1, nmax}], {x, 0, nmax}], x]

Prog

(PARI) m=40; my(x='x+O('x^m)); Vec( 1/prod(k=1, m+2, (1+x^k/(1-x)^k)) ) \\ G. C. Greubel, Apr 03 2019
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( 1/(&*[(1+x^k/(1-x)^k): k in [1..m+2]]) )); // G. C. Greubel, Apr 03 2019
(Sage) m=40; (1/product(1+x^k/(1-x)^k for k in (1..m+2))).series(x, m).coefficients(x, sparse=False) # G. C. Greubel, Apr 03 2019

Crossrefs

Cf. A081362, A129519, A218482, A307310.

Sequence in context: A331173 A307089 A239132 * A272081 A317582 A378758

Adjacent sequences: A307308 A307309 A307310 * A307312 A307313 A307314

Keyword

sign

Author

Ilya Gutkovskiy, Apr 02 2019

Status

approved