A190724 Row sums of Riordan matrix A118384.
1, 4, 20, 106, 576, 3174, 17648, 98746, 555104, 3131854, 17720880, 100507554, 571179792, 3251459670, 18535914480, 105803208906, 604598535360, 3458315246238, 19799128470896, 113441876080306, 650450158678256, 3731985710892454, 21425304596140080
Offset: 0
Keywords
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
Programs
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Mathematica
CoefficientList[Series[(1-7x+Sqrt[1-6x+x^2])/((2-12x)Sqrt[1-6x+x^2]),{x,0,100}],x] -
PARI
x='x+O('x^50); Vec((1-7*x+sqrt(1-6*x+x^2))/((2-12*x)*sqrt(1-6*x+x^2))) \\ G. C. Greubel, Mar 26 2017
Formula
a(n) = (6^n+d(n)-sum(6^(k-1)*d(n-k),k=1..n))/2, where d(n) = central Delannoy number (A001850).
G.f.: (1-7*x+sqrt(1-6*x+x^2))/((2-12*x)*sqrt(1-6*x+x^2)).
Recurrence: (n^2+9*n+20)*a(n+5)-8*(3*n^2+23*n+44)*a(n+4)+2*(108*n^2+683*n+1089)*a(n+3)-2*(435*n^2+2159*n+2716)*a(n+2)+(1367*n^2+4917*n+4366)*a(n+1)-210*(n^2+3*n+2)*a(n)=0.
Conjecture: n*(2*n+3)*a(n) +2*(-12*n^2-15*n+22)*a(n-1) +(74*n^2+73*n-274)*a(n-2) -6*(2*n+5)*(n-2)*a(n-3)=0. - R. J. Mathar, Jul 24 2012
a(n) ~ (2+sqrt(2))/(2*sqrt(3*sqrt(2)-4)) * (3+2*sqrt(2))^n/sqrt(Pi*n). - Vaclav Kotesovec, Oct 20 2012