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

0,1

Comments

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

Links

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

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

Maple

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

Crossrefs

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

Sequence in context: A265467 A252872 A121626 * A226351 A091262 A331862

Adjacent sequences: A038694 A038695 A038696 * A038698 A038699 A038700

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved