This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A026000 a(n) = T(2n, n), where T is the Delannoy triangle (A008288). 3
 1, 5, 41, 377, 3649, 36365, 369305, 3800305, 39490049, 413442773, 4354393801, 46082942185, 489658242241, 5220495115997, 55818956905529, 598318746037217, 6427269150511105, 69175175263888037, 745778857519239785 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Even order terms in the diagonal of rational function 1/(1 - (x + y^2 + x*y^2)). - Gheorghe Coserea, Aug 31 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(n) = ((2*n+3)*(n+1)*A027307(n+1)/2-(3*n+2)*n*A027307(n)) / (5*n+3) (guessed). - Mark van Hoeij, Jul 02 2010 Recurrence: 2*n*(2*n-1)*a(n) = (46*n^2-51*n+15)*a(n-1) - (18*n^2-82*n+85)*a(n-2) - (n-2)*(2*n-5)*a(n-3). - Vaclav Kotesovec, Oct 08 2012 a(n) ~ sqrt(150+70*sqrt(5))*((11+5*sqrt(5))/2)^n/(20*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 08 2012 a(n) = hypergeom([-n, -n, n + 1], [1/2,  1], 1). - Peter Luschny, Mar 14 2018 From Gheorghe Coserea, Aug 31 2018:(Start) G.f.: 1 + serreverse((-(44*x^2 + 88*x + 45) + (10*x + 9)*sqrt(20*x^2 + 44*x + 25))/(8*(x + 1)^2)). G.f. y=A(x) satisfies: 0 = 4*(x^2 + 11*x - 1)*y^3 + (x + 3)*y + 1. 0 = 2*x*(x - 2)*(x^2 + 11*x - 1)*y'' + (5*x^3 + 8*x^2 - 87*x + 2)*y' + (x^2 - 7*x - 10)*y. (End) EXAMPLE A(x) = 1 + 5*x + 41*x^2 + 377*x^3 + 3649*x^4 + 36365*x^5 + ... MATHEMATICA Flatten[{1, RecurrenceTable[{2*n*(2*n-1)*a[n] == (46*n^2-51*n+15)*a[n-1] - (18*n^2-82*n+85)*a[n-2] - (n-2)*(2*n-5)*a[n-3], a[1]==5, a[2]==41, a[3]==377}, a, {n, 20}]}] (* Vaclav Kotesovec, Oct 08 2012 *) a[n_] :=  HypergeometricPFQ[{-n, -n, n + 1}, {1/2, 1}, 1]; Table[a[n], {n, 0, 18}] (* Peter Luschny, Mar 14 2018 *) PROG (PARI) seq(N) = {   my(a = vector(N)); a[1]=5; a[2]=41; a[3]=377;   for (n=4, N,     a[n] = (46*n^2-51*n+15)*a[n-1] - (18*n^2-82*n+85)*a[n-2] - (n-2)*(2*n-5)*a[n-3];     a[n] /= 2*n*(2*n-1));   concat(1, a); }; seq(18) \\ test: y=Ser(seq(303), 'x); 0 == 4*(x^2 + 11*x - 1)*y^3 + (x + 3)*y + 1 \\ Gheorghe Coserea, Aug 31 2018 CROSSREFS Cf. A008288, A027307. Sequence in context: A145215 A083884 A156153 * A058475 A199684 A177506 Adjacent sequences:  A025997 A025998 A025999 * A026001 A026002 A026003 KEYWORD nonn AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 18 20:51 EDT 2019. Contains 327181 sequences. (Running on oeis4.)