|
|
A049428
|
|
Row sums of triangle A049411.
|
|
6
|
|
|
1, 1, 6, 36, 246, 2046, 19716, 209616, 2441916, 31050396, 425883816, 6244077456, 97391939976, 1609040166696, 28029696862896, 512903202039936, 9829166157390096, 196739739722616336, 4102788435212513376, 88945209649582514496, 2000700796384204930656
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: exp((-1+(1+x)^6)/6).
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
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
|
|
MATHEMATICA
|
nmax = 20;
a[n_, m_] := BellY[n, m, Table[k! Binomial[5, k], {k, 0, nmax}]];
a[0] = 1; a[n_] := Sum[a[n, m], {m, 1, n}];
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|