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

%I

%S 1,6,44,360,3152,28896,273856,2661504,26380544,265655808,2710244352,

%T 27952883712,290977271808,3053105307648,32256844087296,

%U 342870535471104,3664053076557824,39342496410894336,424243929700630528,4592400943255388160,49885822426526253056

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

%H Vincenzo Librandi, <a href="/A090442/b090442.txt">Table of n, a(n) for n = 1..200</a>

%H Paul Barry, <a href="https://www.emis.de/journals/JIS/VOL22/Barry3/barry422.html">Generalized Catalan Numbers Associated with a Family of Pascal-like Triangles</a>, J. Int. Seq., Vol. 22 (2019), Article 19.5.8.

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

%F Recurrence: (n+1)*a(n) = 6*(2*n-1)*a(n-1) - 4*(n-2)*a(n-2). - _Vaclav Kotesovec_, Oct 14 2012

%F a(n) ~ sqrt(4+3*sqrt(2))*(6+4*sqrt(2))^n/(8*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 14 2012

%F a(n) = 2^(n-1) * A001003(n) = 2^(n-2) * A006318(n). - _Jacob Post_, Jun 19 2018

%t 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 *)

%Y Cf. A001003, A006318, A090452.

%K nonn,easy

%O 1,2

%A _Wolfdieter Lang_, Dec 23 2003

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Last modified August 18 02:34 EDT 2022. Contains 356204 sequences. (Running on oeis4.)