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A046714 Convolution of A000108 (Catalan) with A000351 (powers of 5). 4
1, 6, 32, 165, 839, 4237, 21317, 107014, 536500, 2687362, 13453606, 67326816, 336842092, 1684953360, 8427441240, 42146901045, 210769862895, 1053978959265, 5270372435025, 26353629438315, 131774711311995 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 16 05:44 EDT 2018. Contains 316259 sequences. (Running on oeis4.)