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A247644 Triangle formed from the even-numbered rows of A088855. 1
1, 1, 1, 1, 1, 2, 4, 2, 1, 1, 3, 9, 9, 9, 3, 1, 1, 4, 16, 24, 36, 24, 16, 4, 1, 1, 5, 25, 50, 100, 100, 100, 50, 25, 5, 1, 1, 6, 36, 90, 225, 300, 400, 300, 225, 90, 36, 6, 1, 1, 7, 49, 147, 441, 735, 1225, 1225, 1225, 735, 441, 147, 49, 7, 1, 1, 8, 64, 224, 784, 1568, 3136, 3920, 4900, 3920, 3136, 1568, 784, 224, 64, 8, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..80.

Johann Cigler, Some remarks and conjectures related to lattice paths in strips along the x-axis, arXiv:1501.04750 [math.CO], 2015-2016.

EXAMPLE

Triangle begins:

1,

1,1,1,

1,2,4,2,1,

1,3,9,9,9,3,1,

1,4,16,24,36,24,16,4,1,

1,5,25,50,100,100,100,50,25,5,1,

1,6,36,90,225,300,400,300,225,90,36,6,1,

1,7,49,147,441,735,1225,1225,1225,735,441,147,49,7,1,

1,8,64,224,784,1568,3136,3920,4900,3920,3136,1568,784,224,64,8,1,

...

MATHEMATICA

row[n_] := CoefficientList[Sum[Binomial[n, k]^2 *x^(2*k), {k, 0, n}] + Sum[Binomial[n, k]*Binomial[n, k - 1]* x^(2*k - 1), {k, 0, n}], x];

Table[row[n], {n, 0, 8}] // Flatten (* Jean-François Alcover, Jun 07 2018 *)

CROSSREFS

Cf. A088855.

Sequence in context: A225812 A132823 A059317 * A220886 A256156 A302828

Adjacent sequences:  A247641 A247642 A247643 * A247645 A247646 A247647

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Sep 23 2014

EXTENSIONS

Row n=8 corrected by Jean-François Alcover, Jun 07 2018

STATUS

approved

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Last modified October 15 11:03 EDT 2018. Contains 316224 sequences. (Running on oeis4.)