A049428 Row sums of triangle A049411.

1, 1, 6, 36, 246, 2046, 19716, 209616, 2441916, 31050396, 425883816, 6244077456, 97391939976, 1609040166696, 28029696862896, 512903202039936, 9829166157390096, 196739739722616336, 4102788435212513376, 88945209649582514496, 2000700796384204930656

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..485

Vladimir Victorovich Kruchinin, Composition of ordinary generating functions, arXiv:1009.2565 [math.CO], 2010.

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)^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

a(n) = Sum_{k=0..n} Stirling1(n,k) * A005012(k). - Seiichi Manyama, Jan 31 2024

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}];
Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Jul 27 2018 *)

Crossrefs

Column k=5 of A293991.

Cf. A005012.

Sequence in context: A354457 A199422 A049431 * A129063 A367260 A366496

Adjacent sequences: A049425 A049426 A049427 * A049429 A049430 A049431

Keyword

easy,nonn

Author

Wolfdieter Lang

Extensions

Offset adjusted by R. J. Mathar, Aug 29 2009

Status

approved