A193684 Alternating row sums of Sheffer triangle A143496 (4-restricted Stirling2 numbers).

1, 3, 8, 17, 17, -78, -585, -2021, -1710, 29395, 231413, 856264, -346979, -30019585, -232782792, -834712259, 2313820717, 59793779314, 469729578123, 1597321309383, -9914171906614, -206169178856073, -1697255630380351, -5677886943413120, 55801423903125353

Offset: 0

Author

Wolfdieter Lang, Oct 06 2011

Keywords

• sign
• easy

Comments

In order to have A143496 as a lower triangular Sheffer matrix one uses row and column offsets 0 (not 4).

Examples

			With offset [0,0] row n=3 of A143496 is [64,61,15,1], hence a(3)=64-61+15-1=17.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..591

Crossrefs

Cf. A143496, A193683 (3-restricted Stirling2 case), A196835, A293037, A346739.

Programs

PARI

my(x='x+O('x^30)); Vec(serlaplace(exp(-exp(x)+4*x+1))) \\ Michel Marcus, Aug 02 2021

Formula

E.g.f.: exp(-exp(x)+4*x+1).

a(n) = exp(1) * Sum_{k>=0} (-1)^k * (k + 4)^n / k!. - Ilya Gutkovskiy, Dec 20 2019

a(0) = 1; a(n) = 4 * a(n-1) - Sum_{k=0..n-1} binomial(n-1,k) * a(k). - Seiichi Manyama, Aug 02 2021