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 A338400 Inverse boustrophedon transform of the partition numbers. 1
 1, 0, 1, -2, 2, -19, 39, -257, 1113, -6829, 42399, -299550, 2281531, -18901042, 168402645, -1608304966, 16381456532, -177291076953, 2031597803009, -24573784682206, 312883002507064, -4182938253898882, 58584703430964506, -857812167322107132, 13106404407407087063 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Eric Weisstein's World of Mathematics, Boustrophedon Transform Wikipedia, Boustrophedon transform FORMULA a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000111(n-k) * A000041(k). PROG (Python) import sympy def A338400(n):   T=[]   for k in range(n+1):     T.append(sympy.npartitions(k))     T.reverse()     for i in range(k):       T[i+1]=T[i]-T[i+1]   return T[-1] (Python) from itertools import islice, count, accumulate from operator import sub from sympy import npartitions def A338400_gen(): # generator of terms     blist = tuple()     for i in count(0):         yield (blist := tuple(accumulate(reversed(blist), func=sub, initial=npartitions(i))))[-1] A338400_list = list(islice(A338400_gen(), 20)) # Chai Wah Wu, Jun 10 2022 CROSSREFS Cf. A000041, A000111, A000751. Sequence in context: A184317 A141084 A172194 * A093777 A326177 A103129 Adjacent sequences:  A338397 A338398 A338399 * A338401 A338402 A338403 KEYWORD sign AUTHOR Pontus von BrÃ¶mssen, Oct 24 2020 STATUS approved

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Last modified July 6 22:19 EDT 2022. Contains 355115 sequences. (Running on oeis4.)