A038697 - OEIS

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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

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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