A026379 a(n) = number of integer strings s(0),...,s(n) counted by array T in A026374 that have s(n)=3; also a(n) = T(2n-1,n-2).

1, 7, 39, 202, 1015, 5028, 24731, 121208, 593019, 2899335, 14173401, 69301422, 338990145, 1659037695, 8124085575, 39806373880, 195160896835, 957396540285, 4699409632805, 23080158080150, 113414575414245, 557601196738190

Offset: 2

Author

Clark Kimberling

Keywords

• nonn
• nice
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..300

Crossrefs

Partial sums of A034942.

Programs

Maple

sum(binomial(n,k)*binomial(2*k+1,k-1),k=0..n); n=0,1,... # N. J. A. Sloane

Mathematica

a[n_] := (n-1)*Hypergeometric2F1[5/2, 2-n, 4, -4]; Table[a[n], {n, 2, 23}](* Jean-François Alcover, Jun 12 2012, after N. J. A. Sloane *)
Table[Sum[Binomial[n,k]Binomial[2k+1,k-1],{k,0,n}],{n,30}] (* Harvey P. Dale, Apr 28 2013  *)

Formula

a(n) = [t^(n+1)]{(1+t)(1+3t+t^2)^(n-1)}. - Emeric Deutsch, Jan 30 2004

G.f.: -1/x+2-2*x^2/(10*x^2+sqrt(1-5*x)*sqrt(1-x)*(4*x-1)-7*x+1). - Vladimir Kruchinin, Aug 11 2015