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
Examples
a(2) = 25 - 11 + 1 = 15.
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..589
Programs
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PARI
my(x='x+O('x^30)); Vec(serlaplace(exp(-exp(x)+5*x+1))) \\ Michel Marcus, Aug 02 2021
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