The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A247644 Triangle formed from the odd-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 1,6 COMMENTS The rows give the coefficients in the numerator polynomials of the o.g.f.s for the columns of triangle A055898. - Georg Fischer, Aug 16 2021 They also occur (with a factor 2*x) in the numerator polynomials of the difference A157052-A157074. - Georg Fischer, Sep 27 2021 LINKS 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 *) PROG (PARI) T(n, k) = binomial((n-1)\2, (k-1)\2)*binomial(n\2, k\2); \\ A088855 row(n) = vector(2*n-1, k, T(2*n-1, k)); \\ Michel Marcus, Sep 27 2021 CROSSREFS Cf. A055899, A055900, A055901, A055902, A055903, A055904, A088855. Cf. A088459 (even numbered rows of A088855). Sequence in context: A132823 A059317 A322046 * A220886 A256156 A342060 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 Offset changed to 1 by Georg Fischer, Sep 27 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 27 06:29 EST 2021. Contains 349363 sequences. (Running on oeis4.)