A054442 Second convolution of A001405 (central binomial numbers).

1, 3, 9, 22, 54, 123, 281, 618, 1362, 2934, 6330, 13452, 28620, 60243, 126921, 265282, 554874, 1153506, 2399390, 4966740, 10286196, 21219038, 43790154, 90076452, 185353204, 380364108, 780786516, 1599015192, 3275589144

Offset: 0

Author

Wolfdieter Lang, Mar 27 2000

Keywords

• easy
• nonn

Crossrefs

Cf. A000108, A001405, A054336, A045621.

Formula

a(2*k)= -3*2^(2*k+1)+binomial(2*(k+1), k+1)*(4*k+7)/2, a(2*k+1)= -3*4^(k+1)+binomial(2*(k+2), k+2)*(2*k+5)/2, k >= 0.

a(n)= A054336(n+2, 2) (third column of convolution triangle). G.f.: (1/(1-x-x^2*c(x^2)))^3, with c(x) the g.f. for the Catalan numbers A000108.