A319360 Expansion of e.g.f. (1 + x)*exp(log(1 + x)^2/2).

1, 1, 1, 0, 2, -10, 64, -476, 4038, -38466, 406446, -4716624, 59621748, -815339460, 11992028112, -188746844040, 3165161922492, -56333871521508, 1060525150393308, -21053827255670976, 439558554065307288, -9627439778044075512, 220722057792327097920, -5286159770781782374800

Offset: 0

Author

Ilya Gutkovskiy, Sep 17 2018

Keywords

• sign

Comments

Inverse Stirling transform of A000085.

Links

• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000085, A004211.

Programs

Maple

seq(n!*coeff(series((1 + x)*exp(log(1 + x)^2/2),x=0,24),x,n),n=0..23); # Paolo P. Lava, Jan 09 2019

Mathematica

nmax = 23; CoefficientList[Series[(1 + x) Exp[Log[1 + x]^2/2], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[StirlingS1[n, k] HypergeometricU[-k/2, 1/2, -1/2]/(-1/2)^(k/2), {k, 0, n}], {n, 0, 23}]

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*A000085(k).