A196835 Alternating row sums of Sheffer triangle A193685 (5-restricted Stirling2 numbers).

1, 4, 15, 51, 146, 273, -319, -6374, -36235, -113833, 69388, 3772035, 28631669, 112704452, -96418909, -5652669753, -50538496446, -230554460867, 281597003109, 16303457144146, 166512491229617, 872578914956059, -1111135578108284, -78512971676777833, -919653124088665479

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..589

Formula

a(n) = Sum_{m=0..n} (-1)^m * A193685(n,m), n>=0.

E.g.f.: exp(-exp(x)+5*x+1).

a(n) = exp(1) * Sum_{k>=0} (-1)^k * (k + 5)^n / k!. - Ilya Gutkovskiy, Dec 20 2019

a(0) = 1; a(n) = 5 * a(n-1) - Sum_{k=0..n-1} binomial(n-1,k) * a(k). - Seiichi Manyama, Aug 02 2021

Example

a(2) = 25 - 11 + 1 = 15.

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp(-exp(x)+5*x+1))) \\ Michel Marcus, Aug 02 2021

Crossrefs

Cf. A193685, A196834 (row sums), A193683, A193684, A293037, A346740.

Sequence in context: A094705 A280786 A283276 * A055218 A303843 A107307

Adjacent sequences: A196832 A196833 A196834 * A196836 A196837 A196838

Keyword

sign,easy

Author

Wolfdieter Lang, Oct 07 2011

Status

approved