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A338400
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Inverse boustrophedon transform of the partition numbers.
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1
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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
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000111(n-k) * A000041(k).
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PROG
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(Python)
import sympy
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]
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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