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A131765 Series reversion of x(1-5x)/(1-x) . 5
1, 4, 36, 404, 5076, 68324, 963396, 14046964, 210062196, 3204118724, 49656709476, 779690085204, 12376867734036, 198301332087204, 3202580085625476, 52080967814444724, 852103170531254196, 14016301507253656964 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The Hankel transform of this sequence is 20^C(n+1,2) .

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n) = Sum_{0<=k<=n} A086810(n,k)*4^k .

From Paul Barry, Sep 08 2009: (Start)

a(n) = Sum_{k=0..n} C(n+k,2k)*A000108(k)*(-1)^(n-k)*5^k};

a(n) = Sum_{k=0..n} C(n+k,2k)*A000108(k)*(4^(k+1)+(-1)^k)/5. (End)

Recurrence: (n+1)*a(n) = 9*(2*n-1)*a(n-1) - (n-2)*a(n-2) . - Vaclav Kotesovec, Oct 20 2012

a(n) ~ sqrt(40+18*sqrt(5))*(9+4*sqrt(5))^n/(10*sqrt(Pi)*n^(3/2)) . - Vaclav Kotesovec, Oct 20 2012

a(n) = Sum_{k=0..n} (-1)^k*binomial(n, k)*hypergeom([k - n, n + 1], [k + 2], -4]. - Peter Luschny, Jan 08 2018

MATHEMATICA

Table[Sum[Binomial[n+k, 2*k]*Binomial[2*k, k]/(k+1)*(-1)^(n-k)*5^k, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 20 2012 *)

a[n_] := Sum[(-1)^k Binomial[n, k] Hypergeometric2F1[k - n, n + 1, k + 2, -4], {k, 0, n}]; Table[a[n], {n, 0, 17}] (* Peter Luschny, Jan 08 2018 *)

PROG

(PARI) Vec(serreverse(x*(1-5*x)/(1-x) + O(x^30))) \\ Michel Marcus, Jan 08 2018

CROSSREFS

Sequence in context: A239112 A002894 A202828 * A244559 A319175 A317147

Adjacent sequences:  A131762 A131763 A131764 * A131766 A131767 A131768

KEYWORD

nonn

AUTHOR

Philippe Deléham, Oct 29 2007

EXTENSIONS

Extra terms added. Paul Barry, Sep 08 2009

STATUS

approved

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Last modified March 25 04:25 EDT 2019. Contains 321457 sequences. (Running on oeis4.)