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A318109 a(n) = Sum_{k=0..n} (3*n-2*k)!/((n-k)!^3*k!)*(-2)^k. 2
1, 4, 46, 652, 10186, 168304, 2884456, 50723824, 909192538, 16538659384, 304391739796, 5655971294824, 105929883322576, 1997228410630912, 37871584674309376, 721672204654077952, 13811327854028171098, 265324110145941691912, 5114208160758838538044, 98874597697991698311832, 1916741738060370782929036 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Diagonal of rational function 1/(1 - (x + y + z - 2*x*y*z)).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..766 (terms 0..100 from Gheorghe Coserea)

FORMULA

G.f. y=A(x) satisfies: 0 = x*(x - 1)*(4*x - 1)*(8*x^2 + 20*x - 1)*y'' + (96*x^4 + 64*x^3 - 120*x^2 + 42*x - 1)*y' + 4*(2*x + 1)*(4*x^2 - 2*x + 1)*y.

EXAMPLE

A(x) = 1 + 4*x + 46*x^2 + 652*x^3 + 10186*x^4 + 168304*x^5 + 2884456*x^6 + ...

PROG

(PARI)

a(n) = sum(k=0, n, (3*n-2*k)!/((n-k)!^3*k!)*(-2)^k);

vector(21, n, a(n-1))

CROSSREFS

Cf. A318107.

Sequence in context: A236956 A113264 A264717 * A234527 A126739 A191870

Adjacent sequences:  A318106 A318107 A318108 * A318110 A318111 A318112

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Sep 20 2018

STATUS

approved

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Last modified October 26 11:59 EDT 2021. Contains 348267 sequences. (Running on oeis4.)