A049427 Row sums of triangle A049424.
1, 1, 5, 25, 145, 1025, 8245, 72745, 704705, 7424065, 83940805, 1012504505, 12972555025, 175624847425, 2501468566325, 37364323364425, 583569693556225, 9504040277271425, 161021013457176325, 2832196631069755225, 51619359912771959825
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..510
- W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
Formula
E.g.f.: exp((-1+(1+x)^5)/5).
a(n) = n! * sum(k=0..n, sum(j=0..k, binomial(5*j,n) * (-1)^(k-j)/(5^k * (k-j)!*j!))). - Vladimir Kruchinin, Feb 07 2011
D-finite with recurrence a(n) -a(n-1) +4*(-n+1)*a(n-2) -6*(n-1)*(n-2)*a(n-3) -4*(n-1)*(n-2)*(n-3)*a(n-4) -(n-1)*(n-2)*(n-3)*(n-4)*a(n-5)=0. - R. J. Mathar, Jun 23 2023
a(n) = Sum_{k=0..n} Stirling1(n,k) * A005011(k). - Seiichi Manyama, Jan 31 2024
a(n) = (1/exp(1/5)) * n! * Sum_{k>=0} binomial(5*k,n)/(5^k * k!). - Seiichi Manyama, Jan 18 2025