A307259 Expansion of (1/(1 - x)) * Product_{k>=1} (1 + k*x^k/(1 - x)^k).

1, 2, 5, 15, 44, 126, 357, 1003, 2783, 7618, 20627, 55421, 148021, 393140, 1038123, 2724992, 7112022, 18465708, 47726767, 122861732, 315123476, 805428727, 2051556778, 5207982062, 13177117709, 33235023381, 83574705456, 209576713721, 524181331710, 1307849984089, 3255539133109

Offset: 0

Author

Ilya Gutkovskiy, Apr 01 2019

Keywords

• nonn

Comments

Binomial transform of A022629.

Crossrefs

Cf. A022629, A266232, A294502, A307260, A318127.

Programs

Maple

a:=series((1/(1-x))*mul(1+k*x^k/(1-x)^k,k=1..100),x=0,31): seq(coeff(a,x,n),n=0..30); # Paolo P. Lava, Apr 03 2019

Mathematica

nmax = 30; CoefficientList[Series[1/(1 - x) Product[(1 + k x^k/(1 - x)^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) = Sum_{k=0..n} binomial(n,k)*A022629(k).