A090442 Row sums of array A090452 (s2_{3,2}, scaled (3,2)-Stirling2).

1, 6, 44, 360, 3152, 28896, 273856, 2661504, 26380544, 265655808, 2710244352, 27952883712, 290977271808, 3053105307648, 32256844087296, 342870535471104, 3664053076557824, 39342496410894336, 424243929700630528, 4592400943255388160, 49885822426526253056

Offset: 1

Author

Wolfdieter Lang, Dec 23 2003

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Paul Barry, Generalized Catalan Numbers Associated with a Family of Pascal-like Triangles, J. Int. Seq., Vol. 22 (2019), Article 19.5.8.

Crossrefs

Cf. A001003, A006318, A090452.

Programs

Mathematica

RecurrenceTable[{(n+1)*a[n] == 6*(2*n-1)*a[n-1] - 4*(n-2)*a[n-2],a[1]==1,a[2]==6},a,{n,20}] (* Vaclav Kotesovec, Oct 14 2012 *)

Formula

a(n) = Sum_{m=2..2*n} A090452(n, m).

Recurrence: (n+1)*a(n) = 6*(2*n-1)*a(n-1) - 4*(n-2)*a(n-2). - Vaclav Kotesovec, Oct 14 2012

a(n) ~ sqrt(4+3*sqrt(2))*(6+4*sqrt(2))^n/(8*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 14 2012

a(n) = 2^(n-1) * A001003(n) = 2^(n-2) * A006318(n). - Jacob Post, Jun 19 2018