A299211 Expansion of 1/(1 - x*Product_{k>=1} (1 - x^k)^k).

1, 1, 0, -3, -6, -4, 12, 39, 52, -9, -186, -392, -285, 610, 2291, 3200, -150, -10626, -23487, -18841, 32957, 134848, 198246, 13961, -605248, -1409604, -1234474, 1744213, 7898753, 12209679, 2161666, -34344627, -84393284, -79993042, 90692470, 461463974, 749309529, 207447895, -1939084232

Offset

0,4

Links

Robert Israel, Table of n, a(n) for n = 0..3925

N. J. A. Sloane, Transforms

Formula

G.f.: 1/(1 - x*Product_{k>=1} (1 - x^k)^k).

a(0) = 1; a(n) = Sum_{k=1..n} A073592(k-1)*a(n-k).

Maple

N:= 100: # for a(0)..a(N)
S:= series(1/(1-x*mul((1-x^k)^k, k=1..N)), x, N+1):
seq(coeff(S, x, i), i=0..N); # Robert Israel, Feb 05 2023

Mathematica

nmax = 38; CoefficientList[Series[1/(1 - x Product[(1 - x^k)^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Antidiagonal sums of A276554.

Cf. A067687, A073592, A299105, A299106, A299108, A299162, A299164, A299166, A299167, A299208, A299209, A299210, A299212.

Sequence in context: A328637 A162523 A292681 * A067979 A091808 A357235

Adjacent sequences: A299208 A299209 A299210 * A299212 A299213 A299214

Keyword

sign

Author

Ilya Gutkovskiy, Feb 05 2018

Status

approved