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A049428 Row sums of triangle A049411.

%I A049428 #29 Jan 18 2025 09:04:25
%S A049428 1,1,6,36,246,2046,19716,209616,2441916,31050396,425883816,6244077456,
%T A049428 97391939976,1609040166696,28029696862896,512903202039936,
%U A049428 9829166157390096,196739739722616336,4102788435212513376,88945209649582514496,2000700796384204930656
%N A049428 Row sums of triangle A049411.
%H A049428 Seiichi Manyama, <a href="/A049428/b049428.txt">Table of n, a(n) for n = 0..485</a>
%H A049428 Vladimir Victorovich Kruchinin, <a href="http://arxiv.org/abs/1009.2565">Composition of ordinary generating functions</a>, arXiv:1009.2565 [math.CO], 2010.
%H A049428 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 A049428 E.g.f.: exp((-1+(1+x)^6)/6).
%F A049428 a(n) = n! * Sum_{k=1..n} Sum_{j=0..k} binomial(6*j,n) *(-1)^(k-j)/ (6^k*(k-j)!*j!). - _Vladimir Kruchinin_, Feb 07 2011
%F A049428 D-finite with recurrence a(n) -a(n-1) +5*(-n+1)*a(n-2) -10*(n-1)*(n-2)*a(n-3) -10*(n-1)*(n-2)*(n-3)*a(n-4) -5*(n-1)*(n-2)*(n-3)*(n-4)*a(n-5) -(n-5)*(n-1)*(n-2)*(n-3)*(n-4)*a(n-6)=0. - _R. J. Mathar_, Jun 23 2023
%F A049428 a(n) = Sum_{k=0..n} Stirling1(n,k) * A005012(k). - _Seiichi Manyama_, Jan 31 2024
%F A049428 a(n) = (1/exp(1/6)) * n! * Sum_{k>=0} binomial(6*k,n)/(6^k * k!). - _Seiichi Manyama_, Jan 18 2025
%t A049428 nmax = 20;
%t A049428 a[n_, m_] := BellY[n, m, Table[k! Binomial[5, k], {k, 0, nmax}]];
%t A049428 a[0] = 1; a[n_] := Sum[a[n, m], {m, 1, n}];
%t A049428 Table[a[n], {n, 0, nmax}] (* _Jean-François Alcover_, Jul 27 2018 *)
%Y A049428 Column k=5 of A293991.
%Y A049428 Cf. A005012.
%K A049428 easy,nonn
%O A049428 0,3
%A A049428 _Wolfdieter Lang_
%E A049428 Offset adjusted by _R. J. Mathar_, Aug 29 2009