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A338400 Inverse boustrophedon transform of the partition numbers.

%I A338400 #9 Jun 11 2022 01:19:51
%S A338400 1,0,1,-2,2,-19,39,-257,1113,-6829,42399,-299550,2281531,-18901042,
%T A338400 168402645,-1608304966,16381456532,-177291076953,2031597803009,
%U A338400 -24573784682206,312883002507064,-4182938253898882,58584703430964506,-857812167322107132,13106404407407087063
%N A338400 Inverse boustrophedon transform of the partition numbers.
%H A338400 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BoustrophedonTransform.html">Boustrophedon Transform</a>
%H A338400 Wikipedia, <a href="https://en.wikipedia.org/wiki/Boustrophedon_transform">Boustrophedon transform</a>
%H A338400 <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>
%F A338400 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000111(n-k) * A000041(k).
%o A338400 (Python)
%o A338400 import sympy
%o A338400 def A338400(n):
%o A338400   T=[]
%o A338400   for k in range(n+1):
%o A338400     T.append(sympy.npartitions(k))
%o A338400     T.reverse()
%o A338400     for i in range(k):
%o A338400       T[i+1]=T[i]-T[i+1]
%o A338400   return T[-1]
%o A338400 (Python)
%o A338400 from itertools import islice, count, accumulate
%o A338400 from operator import sub
%o A338400 from sympy import npartitions
%o A338400 def A338400_gen(): # generator of terms
%o A338400     blist = tuple()
%o A338400     for i in count(0):
%o A338400         yield (blist := tuple(accumulate(reversed(blist),func=sub,initial=npartitions(i))))[-1]
%o A338400 A338400_list = list(islice(A338400_gen(),20)) # _Chai Wah Wu_, Jun 10 2022
%Y A338400 Cf. A000041, A000111, A000751.
%K A338400 sign
%O A338400 0,4
%A A338400 _Pontus von Brömssen_, Oct 24 2020