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

0,3

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.

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

Cf. A004213, A049410.

Column of A293991.

Sequence in context: A200725 A255906 A260949 * A345889 A057725 A196192

Adjacent sequences: A049423 A049424 A049425 * A049427 A049428 A049429

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved