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A051643 Central elements in Parker's partition triangle. 0
1, 3, 20, 169, 1667, 18084, 208960, 2527074, 31630390, 406680465, 5342750699, 71442850111, 969548468960, 13323571588607, 185072895183632, 2594890728951909, 36681505784903758, 522291180086851188 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

R. K. Guy, Parker's permutation problem involves the Catalan numbers, Amer. Math. Monthly 100 (1993), 287-289.

FORMULA

a(n) = coefficient of q^((n^2-1)/2) in q-binomial coefficient [2n, n].

MATHEMATICA

a[n_] := SeriesCoefficient[QBinomial[2(2n+1), 2n+1, q], {q, 0, 2n(n+1)}];

Table[a[n], {n, 0, 17}] (* Jean-Fran├žois Alcover, Aug 19 2019 *)

CROSSREFS

Cf. A047812, A007042.

Sequence in context: A063017 A276315 A145329 * A213377 A216583 A154644

Adjacent sequences:  A051640 A051641 A051642 * A051644 A051645 A051646

KEYWORD

easy,nonn,nice

AUTHOR

James A. Sellers

STATUS

approved

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Last modified November 19 06:03 EST 2019. Contains 329310 sequences. (Running on oeis4.)