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A118346 Central terms of pendular triangle A118345. 6
1, 1, 5, 30, 201, 1445, 10900, 85128, 682505, 5585115, 46461437, 391743850, 3340361700, 28755475180, 249572076200, 2181469638880, 19186562661273, 169677521094215, 1507881643936015, 13458730170115778, 120599648894147185 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also, g.f. A(x) = (1/x)*series_reversion of x/(1 + x*GF(A005572)), where GF(A005572) is the g.f. of A005572, which is the number of walks on cubic lattice starting and finishing on the xy plane and never going below it.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

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

G.f.: A(x) = 1 + series_reversion[x/((1+x)*(1+4*x+x^2))].

G.f.: A(x) = (1/x)*series_reversion[ x*(1-2*x+sqrt((1-2*x)*(1-6*x)))/2/(1-2*x) ].

For n>0: a(n) = (1/n)*sum(binomial(n,j)*sum(binomial(j,i)*binomial(n-j,2*j-n-i-1)*5^(2*n-3*j+2*i+1),i=0..n-1), j=0..n). [Vladimir Kruchinin, Dec 26 2010]

PROG

(PARI) {a(n)=polcoeff(serreverse(x*(1-2*x+sqrt((1-2*x)*(1-6*x)+x*O(x^n)))/2/(1-2*x))/x, n)}

CROSSREFS

Cf. A118345, A118347, A118348, A118349.

Sequence in context: A196678 A128328 A245376 * A234422 A091927 A253076

Adjacent sequences:  A118343 A118344 A118345 * A118347 A118348 A118349

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 26 2006

STATUS

approved

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Last modified January 21 19:33 EST 2021. Contains 340352 sequences. (Running on oeis4.)