login
A049426
Row sums of triangle A049410.
6
1, 1, 4, 16, 76, 436, 2776, 19384, 148576, 1226656, 10824256, 101695936, 1010783104, 10577428096, 116166090496, 1334409569536, 15985101216256, 199216504113664, 2577292524107776, 34542575915216896, 478781761481291776
OFFSET
0,3
LINKS
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)^4)/4).
a(n) = n!*Sum_(k=1..n, Sum_(j=0..k, binomial(4*j,n)*(-1)^(k-j)/(4^k*(k-j)!*j!))). - Vladimir Kruchinin, Feb 07 2011
D-finite with recurrence a(n) -a(n-1) +3*(-n+1)*a(n-2) -3*(n-1)*(n-2)*a(n-3) -(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Jun 23 2023
a(n) = Sum_{k=0..n} Stirling1(n,k) * A004213(k). - Seiichi Manyama, Jan 31 2024
MATHEMATICA
With[{nn=20}, CoefficientList[Series[Exp[((1+x)^4-1)/4], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Jan 28 2017 *)
CROSSREFS
Column of A293991.
Sequence in context: A200725 A255906 A260949 * A345889 A057725 A196192
KEYWORD
easy,nonn
STATUS
approved