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A190737 Diagonal sums of the Riordan matrix A104259. 2
1, 2, 6, 19, 66, 244, 946, 3801, 15697, 66234, 284339, 1237983, 5453611, 24263355, 108865901, 492051006, 2238220336, 10238568080, 47070014643, 217363784060, 1007794226777, 4689545704246, 21893712581740, 102520882301832, 481393173378979 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: (1-x-2*x^2-sqrt(1-6*x+5*x^2))/(2*x*(1-2*x+x^2+x^3)).
Recurrence: 0 = (n^2+17*n+72)*a(n+8) - (11*n^2+169*n+648)*a(n+7) + 3*(17*n^2+227*n+758)*a(n+6) - 2*(73*n^2+812*n+2259)*a(n+5)
+ 6*(41*n^2+375*n+846)*a(n+4) - (217*n^2+1559*n+2634)*a(n+3) + 3*(17*n^2+29*n-136)*a(n+2) + 10*(5*n^2+43*n+84)*a(n+1) - 25*(n^2+5*n+6)*a(n).
D-finite with recurrence: (n+1)*a(n) +(-8*n+1)*a(n-1) +3*(6*n-5)*a(n-2) +3*(-5*n+8)*a(n-3) +(-n-7)*a(n-4) +5*(n-2)*a(n-5)=0. - R. J. Mathar, Feb 24 2020
MATHEMATICA
CoefficientList[Series[(1-x-2x^2-Sqrt[1-6x+5x^2])/(2x(1-2x+x^2+x^3)), {x, 0, 24}], x]
PROG
(PARI) x='x+O('x^30); Vec((1-x-2*x^2-sqrt(1-6*x+5*x^2))/(2*x*(1-2*x +x^2 +x^3))) \\ G. C. Greubel, Apr 23 2018
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); Coefficients(R!((1-x-2*x^2-Sqrt(1-6*x+5*x^2))/(2*x*(1-2*x+x^2+x^3)))); // G. C. Greubel, Apr 23 2018
CROSSREFS
Sequence in context: A150089 A150090 A150091 * A150092 A150093 A150094
KEYWORD
nonn
AUTHOR
Emanuele Munarini, May 18 2011
STATUS
approved

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Last modified June 17 23:25 EDT 2024. Contains 373468 sequences. (Running on oeis4.)