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A249792 G.f.: Sum_{n>=0} x^n/(1-x)^(4*n) * Sum_{k=0..n} C(n,k)^2 * x^k. 3
1, 1, 6, 27, 121, 555, 2586, 12182, 57867, 276694, 1330065, 6421593, 31117227, 151254410, 737182800, 3601225529, 17628257696, 86446992591, 424605995273, 2088554115971, 10286486862120, 50722097552200, 250374625243921, 1237104826795590, 6118018894827333, 30281155790249615, 149990627879008797 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Limit a(n)/a(n+1) = 0.1980622641951617475..., a root of 1 - 6*x + 5*x^2 - x^3 = 0.

LINKS

Table of n, a(n) for n=0..26.

FORMULA

G.f.: (1-x)^3 / sqrt((1 - 2*x + x^2 - x^3)*(1 - 6*x + 5*x^2 - x^3)).

G.f.: (1-x)^3 / sqrt(1 - 8*x + 18*x^2 - 18*x^3 + 13*x^4 - 6*x^5 + x^6).

EXAMPLE

G.f.: A(x) = 1 + x + 6*x^2 + 27*x^3 + 121*x^4 + 555*x^5 + 2586*x^6 +...

where

A(x) = 1 + x/(1-x)^4*(1+x) + x^2/(1-x)^8*(1+2^2*x+x^2) + x^3/(1-x)^12*(1+3^2*x+3^2*x^2+x^3) + x^4/(1-x)^16*(1+4^2*x+6^2*x^2+4^2*x^3+x^4) + x^5/(1-x)^20*(1+5^2*x+10^2*x^2+10^2*x^3+5^2*x^4+x^5) +...

PROG

(PARI) {a(n)=polcoeff( sum(m=0, n, x^m * sum(k=0, m, binomial(m, k)^2 * x^k) / (1-x +x*O(x^n))^(4*m)), n)}

for(n=0, 30, print1(a(n), ", "))

(PARI) {a(n)=polcoeff( (1-x)^3 / sqrt(1 - 8*x + 18*x^2 - 18*x^3 + 13*x^4 - 6*x^5 + x^6 +x*O(x^n)), n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A249946, A249793, A249794.

Sequence in context: A079762 A175716 A178935 * A002912 A030297 A045500

Adjacent sequences:  A249789 A249790 A249791 * A249793 A249794 A249795

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 12 2014

STATUS

approved

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Last modified October 30 18:13 EDT 2020. Contains 338090 sequences. (Running on oeis4.)