A029887 A sum over scaled A000531 related to Catalan numbers C(n).

1, 11, 82, 515, 2934, 15694, 80324, 397923, 1922510, 9105690, 42438076, 195165646, 887516252, 3997537980, 17857602568, 79200753059, 349051186494, 1529735010658, 6670733733260, 28959032959962, 125209652884756, 539384745200516, 2315840230811832, 9912689725127950

Offset

0,2

Comments

Related to planar maps? - see A000184. - N. J. A. Sloane, Mar 11 2007

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

a(n) = 4^n*sum(A000531(k+1)/4^k, k=0..n) = (2*n+1)*(2*n+3)*(2*n+5)*C(n)/3-(n+2)*2^(2*n+1); a(n)=4*a(n-1)+A000531(n+1).

G.f. c(x)/(1-4*x)^(5/2) = (2-c(x))/(1-4*x)^3, where c(x) = g.f. for Catalan numbers; also convolution of Catalan numbers with A002802.

G.f.: (4*x-1+sqrt(1-4*x))/(2*x*(1-4*x)^3). - Vincenzo Librandi, Mar 14 2014

Mathematica

a[n_] := (2*n+1)*(2*n+3)*(2*n+5)*CatalanNumber[n]/3 - (n+2)*2^(2*n+1); Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Mar 12 2014 *)
CoefficientList[Series[(4 x - 1 + Sqrt[1 - 4 x])/(2 x (1 - 4 x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Mar 14 2014 *)

Prog

(Magma) [(2*n+1)*(2*n+3)*(2*n+5)*Catalan(n)/3 - (n+2)*2^(2*n+1): n in [0..30]]; // Vincenzo Librandi, Mar 14 2014

Crossrefs

Cf. A000184, A000531, A000108, A002802.

Sequence in context: A197643 A261391 A211845 * A026871 A123367 A177142

Adjacent sequences: A029884 A029885 A029886 * A029888 A029889 A029890

Keyword

nonn

Author

Wolfdieter Lang

Extensions

More terms from Vincenzo Librandi, Mar 14 2014

Status

approved