A049426 Row sums of triangle A049410.
1, 1, 4, 16, 76, 436, 2776, 19384, 148576, 1226656, 10824256, 101695936, 1010783104, 10577428096, 116166090496, 1334409569536, 15985101216256, 199216504113664, 2577292524107776, 34542575915216896, 478781761481291776
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..547
- W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.
Programs
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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 *)
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
a(n) = (1/exp(1/4)) * n! * Sum_{k>=0} binomial(4*k,n)/(4^k * k!). - Seiichi Manyama, Jan 18 2025