A339150 - OEIS

A339150

a(n) = Sum_{k=1..n} floor(k/2)! * floor((n - k)/2)! binomial((n-floor(k/2)-1), n-k).

1, 2, 3, 6, 12, 26, 62, 148, 396, 1044, 3024, 8784, 26928, 85824, 274320, 954720, 3149280, 11910240, 40253760, 164643840, 567181440, 2497703040, 8736698880, 41250263040, 146090649600, 736680268800, 2635858713600, 14145091430400, 51047113420800, 290574650419200

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..30.

Jonathan Fang, Zachary Hamaker, and Justin Troyka, On pattern avoidance in matchings and involutions, arXiv:2009.00079 [math.CO], 2020. See Theorem 1.6 (c).

MATHEMATICA

Array[Sum[Floor[k/2]! Floor[(# - k)/2]! Binomial[(# - Floor[k/2] - 1), # - k], {k, #}] &, 30]

PROG

(PARI) a(n) = sum(k=1, n, (k\2)! * ((n-k)\2)! * binomial(n-k\2-1, n-k)); \\ Michel Marcus, Nov 25 2020

CROSSREFS

Sequence in context: A152172 A001677 A373182 * A024422 A186771 A019525

Adjacent sequences: A339147 A339148 A339149 * A339151 A339152 A339153

KEYWORD

nonn

AUTHOR

Michael De Vlieger, Nov 25 2020

STATUS

approved