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%I #23 Feb 26 2020 07:16:04
%S 0,2,6,20,56,120,792,364,560,8568,1140,1540,42504,2600,98280,2035800,
%T 4960,5984,376992,12620256,9880,850668,13244,15180,1712304,19600,
%U 2598960,177100560,27720,4582116,386206920,37820,41664,8936928,969443904,54740,13991544
%N Minimal prime partition representation of even integers.
%C A partition is prime if all parts are primes. A partition of an even integer n > 2 is minimal if it has at most two parts, one of which is the greatest prime less than n - 1. The terms of the sequence are the multinomials of these partition. By convention a(0) = 0 and a(1) = 2.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimePartition.html">Prime Partition</a>
%F For n >= 2 let a(n) be the multinomial of P where P is the partition [p, 2n - p] with p the greatest prime less than 2n - 1.
%e n 2n partition a(n)
%e 2 4 : [2, 2] 6
%e 3 6 : [3, 3] 20
%e 4 8 : [5, 3] 56
%e 5 10: [7, 3] 120
%e 6 12: [7, 5] 792
%e 7 14: [11, 3] 364
%e 8 16: [13, 3] 560
%e 9 18: [13, 5] 8568
%e 10 20: [17, 3] 1140
%e 11 22: [19, 3] 1540
%e 12 24: [19, 5] 42504
%e 13 26: [23, 3] 2600
%e 14 28: [23, 5] 98280
%e 15 30: [23, 7] 2035800
%o (SageMath)
%o def a(n):
%o if n < 2: return 2*n
%o p = previous_prime(2*n - 1)
%o return multinomial([p, 2*n - p])
%o print([a(n) for n in range(40)])
%Y Cf. A327413.
%K nonn
%O 0,2
%A _Peter Luschny_, Sep 07 2019
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