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A356900
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a(n) = P(n, 1/2) where P(n, x) = x^(-n)*Sum_{k=0..n} A241171(n, k)*x^k.
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0
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1, 1, 8, 154, 5552, 321616, 27325088, 3200979664, 494474723072, 97390246272256, 23820397371219968, 7083386168647642624, 2516691244849530785792, 1052914814802404260765696, 512347915163742179541659648, 286902390859642414913802102784, 183187476890368376930869730803712
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OFFSET
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0,3
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COMMENTS
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Other special values of this Euler type polynomials are: P(n, -1) = A000364(n); P(n, -1/2) = A002105(n); P(n, 1) = A094088(n), where we always make the assumption that the offset of the sequences is 0. A partition refinement of Joffe's triangle A241171 is A327022.
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LINKS
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MAPLE
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a := n -> 2^n*add(A241171(n, k)*(1/2)^k, k = 0..n):
seq(a(n), n = 0..16);
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PROG
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(SageMath) # Using function PtransMatrix from A269941.
def E(n, v):
eulr = lambda n: 1 / ((2 * n - 1) * (2 * n))
norm = lambda n, k: (1 / v)^n * factorial(2 * n)
P = PtransMatrix(n, eulr, norm)
return [(-1)^j * sum([v^k * P[j][k] for k in range(j + 1)]) for j in range(n)]
A356900List = lambda n: E(n, -1/2); print(A356900List(17))
# A002105List = lambda n: E(n, 1/2) returns the reduced tangent numbers A002105.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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