A049427 Row sums of triangle A049424.

1, 1, 5, 25, 145, 1025, 8245, 72745, 704705, 7424065, 83940805, 1012504505, 12972555025, 175624847425, 2501468566325, 37364323364425, 583569693556225, 9504040277271425, 161021013457176325, 2832196631069755225, 51619359912771959825

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..510

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)^5)/5).

a(n) = n! * sum(k=0..n, sum(j=0..k, binomial(5*j,n) * (-1)^(k-j)/(5^k * (k-j)!*j!))). - Vladimir Kruchinin, Feb 07 2011

D-finite with recurrence a(n) -a(n-1) +4*(-n+1)*a(n-2) -6*(n-1)*(n-2)*a(n-3) -4*(n-1)*(n-2)*(n-3)*a(n-4) -(n-1)*(n-2)*(n-3)*(n-4)*a(n-5)=0. - R. J. Mathar, Jun 23 2023

a(n) = Sum_{k=0..n} Stirling1(n,k) * A005011(k). - Seiichi Manyama, Jan 31 2024

Crossrefs

Column of A293991.

Row sums of A157394.

Cf. A005011.

Sequence in context: A366221 A371725 A366499 * A121639 A098349 A098212

Adjacent sequences: A049424 A049425 A049426 * A049428 A049429 A049430

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved