A046714 Convolution of A000108 (Catalan) with A000351 (powers of 5).

1, 6, 32, 165, 839, 4237, 21317, 107014, 536500, 2687362, 13453606, 67326816, 336842092, 1684953360, 8427441240, 42146901045, 210769862895, 1053978959265, 5270372435025, 26353629438315, 131774711311995

Offset

0,2

Comments

i) Homogeneous recursion: a(n) = (3*(3*n+1)/(n+1))*a(n-1)-(10*(2*n-1)/(n+1))*a(n-2), a(-1) := 0, a(0)=1, n >= 1. ii) Hypergeometric 2F1 form: 2*a(n) = 5^(n+1)-binomial(2*(n+1), n+1)*hypergeom([ -n-1,1 ],[ 1/2 ],-1/4).

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = sum(C(k)*5^(n-k), k=0..n), C(k)=A000108(k) (Catalan); a(n) = 5*a(n-1)+ C(n), a(0)=1; G.f.: c(x)/(1-5*x), where c(x) = g.f. for Catalan numbers A000108.

a(n) ~ (5-sqrt(5))/2 * 5^n. - Vaclav Kotesovec, Jul 07 2016

Crossrefs

Cf. A000108, A000351.

Sequence in context: A083320 A097139 A034942 * A129171 A082585 A084326

Adjacent sequences: A046711 A046712 A046713 * A046715 A046716 A046717

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved