A038697 Convolution of A000917 with A000984 (central binomial coefficients).

3, 26, 163, 894, 4558, 22196, 104739, 483062, 2189530, 9789900, 43295118, 189749676, 825364668, 3567219688, 15332925731, 65591312550, 279415474594, 1185903736412, 5016725589402, 21159849864964, 89012979703940

Offset: 0

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

Also convolution of A007054 (Super ballot numbers) with A002697;

Links

• Robert Israel, Table of n, a(n) for n = 0..1652

Crossrefs

Cf. A007054, A038665, A038679, A000917, A000108, A000984, A002697.

Programs

Maple

seq(n*4^(n+1)+binomial(2*n+3,n+1),n=0..30); # Robert Israel, May 22 2019

Formula

a(n) = n*4^(n+1)+binomial(2*n+3, n+1).

G.f.: c(x)*(4-c(x))/(1-4*x)^2, where c(x) = g.f. for Catalan numbers A000108.

(160+64*n)*a(n) - (160+48*n)*a(n+1) + (50+12*n)*a(n+2) - (5+n)*a(n+3)=0. - Robert Israel, May 22 2019