A306665 Expansion of Sum_{k>=0} k! * x^(k*(k+1)/2) / Product_{j=1..k} (1 - x^j)^j.

1, 1, 1, 3, 3, 7, 13, 19, 31, 57, 99, 145, 253, 391, 661, 1071, 1647, 2617, 4189, 6439, 10183, 15999, 24195, 37537, 57553, 87925, 132841, 202899, 306147, 458827, 688501, 1030147, 1533535, 2280549, 3370947, 4986265, 7354573, 10779763, 15804901, 23102271, 33685239

Offset

0,4

Links

Table of n, a(n) for n=0..40.

Mathematica

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

Crossrefs

Cf. A032020, A204858, A206138.

Sequence in context: A051123 A096188 A187873 * A065876 A204858 A095008

Adjacent sequences: A306662 A306663 A306664 * A306666 A306667 A306668

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 04 2019

Status

approved