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A294159 Alternating row sums of triangle A291844. 3
1, 1, 2, 6, 18, 55, 171, 538, 1708, 5461, 17560, 56728, 183973, 598597, 1953145, 6388376, 20939664, 68764283, 226192964, 745146462, 2458020664, 8118111977, 26841209903, 88835163150, 294284206183, 975699571009, 3237456793478, 10749922312752, 35718863630895, 118757413662397 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 0..303

FORMULA

G.f. y(x) satisfies: 0 = (x^3 + x^2 + 3*x - 1)*(y^2 - y) + x.

PROG

(PARI)

A291843_ser(N, t='t) = {

  my(x='x+O('x^N), y=1, y1=0, n=1,

  dn = 1/(-2*t^2*x^4 - (2*t^2+3*t)*x^3 - (2*t+1)*x^2 + (2*t-1)*x + 1));

  while (n++,

   y1 = (2*x^2*y'*((-t^2 + t)*x + (-t + 1) + (t^2*x^2 + (t^2 + t)*x + t)*y) +

        (t*x^2 + t*x)*y^2 - (2*t^2*x^3 + 3*t*x^2 + (-t + 1)*x - 1))*dn;

   if (y1 == y, break); y = y1; ); y;

};

A291844_ser(N, t='t) = {

  my(z = A291843_ser(N+1, t));

  ((1+x)*z - 1)*(1 + t*x)/((1-t + t*(1+x)*z)*x*z^2);

};

Vec(A291844_ser(30, -1))

\\ test: y=A291844_ser(200, -1); 0==(x^3 + x^2 + 3*x - 1)*(y^2 - y) + x

CROSSREFS

Cf. A291844.

Sequence in context: A094590 A004529 A238236 * A000778 A006725 A066158

Adjacent sequences:  A294156 A294157 A294158 * A294160 A294161 A294162

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Nov 03 2017

STATUS

approved

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Last modified June 4 00:49 EDT 2020. Contains 334808 sequences. (Running on oeis4.)