0,1

Comment from wolfdieter.lang(AT)physik.uni-karlsruhe.de: G.f.: c(x)*(4-c(x))/(1-4*x)^(3/2), c(x) = g.f. for Catalan numbers A000108 (agrees with Han 75 99, (5.27.9). Convolution of A038679 with A000984 (central binomial coefficients); also convolution of A038665 with A000302 (powers of 4).

Appears as diagonal in A003506. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 12 2006

E. R. Hansen, A Table of Series and Products, Prentice-Hall, Englewood Cliffs, NJ, 1975, p. 99.

a:=proc(n) if n=1 then 3 else binomial(2*n+1, n+1)*n fi end: seq(a(n), n=0..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 26 2006

seq((n-1)*binomial(2*n, n)/2, n=2..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 28 2007

a:=n->add(binomial(2*n, n)/2, k=2..n): seq(a(n), n=2..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 03 2007

a:=n->abs(sum((binomial(-n, n-4)), j=2..n)): seq(a(n), n=4..24); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 03 2007

Cf. A007054, A038665, A038679, A000108, A000984, A000302. 1/beta(n, n+2) in A061928.

Cf. A003506.

Cf. A000984.

Adjacent sequences: A000914 A000915 A000916 this_sequence A000918 A000919 A000920

Sequence in context: A015529 A000948 A074831 this_sequence A025535 A119693 A139471

nonn

njas