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%I #23 Jan 31 2024 08:05:03
%S 1,1,5,25,145,1025,8245,72745,704705,7424065,83940805,1012504505,
%T 12972555025,175624847425,2501468566325,37364323364425,
%U 583569693556225,9504040277271425,161021013457176325,2832196631069755225,51619359912771959825
%N Row sums of triangle A049424.
%H Seiichi Manyama, <a href="/A049427/b049427.txt">Table of n, a(n) for n = 0..510</a>
%H W. Lang, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/LANG/lang.html">On generalizations of Stirling number triangles</a>, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
%F E.g.f.: exp((-1+(1+x)^5)/5).
%F 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
%F 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
%F a(n) = Sum_{k=0..n} Stirling1(n,k) * A005011(k). - _Seiichi Manyama_, Jan 31 2024
%Y Column of A293991.
%Y Row sums of A157394.
%Y Cf. A005011.
%K easy,nonn
%O 0,3
%A _Wolfdieter Lang_
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