A331337 L.g.f.: log(Sum_{k>=0} k! * x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j)).

1, 1, 7, 1, 11, 25, 15, 17, -11, 241, -87, 217, -467, 645, 707, -159, 35, -1451, 4067, -9679, 17661, -19755, 42413, -55615, 31061, -59799, 28231, 147841, -230549, 473185, -1013017, 1656385, -2771619, 3637865, -4581335, 6366313, -5062635, -1059971, 8699659, -22821903

Offset

1,3

Links

Table of n, a(n) for n=1..40.

Formula

exp(Sum_{n>=1} a(n) * x^n / n) = g.f. of A032020.

a(n) = n * A032020(n) - Sum_{k=1..n-1} A032020(k) * a(n-k).

Mathematica

nmax = 40; CoefficientList[Series[Log[Sum[k! x^(k (k + 1)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}]], {x, 0, nmax}], x] Range[0, nmax] // Rest

Crossrefs

Cf. A000593, A032020, A331336.

Sequence in context: A061195 A232111 A074283 * A211836 A165949 A322565

Adjacent sequences: A331334 A331335 A331336 * A331338 A331339 A331340

Keyword

sign

Author

Ilya Gutkovskiy, Jan 14 2020

Status

approved