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A350972
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E.g.f. = tan(x).
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3
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0, 1, 0, 2, 0, 16, 0, 272, 0, 7936, 0, 353792, 0, 22368256, 0, 1903757312, 0, 209865342976, 0, 29088885112832, 0, 4951498053124096, 0, 1015423886506852352, 0, 246921480190207983616, 0, 70251601603943959887872, 0, 23119184187809597841473536, 0, 8713962757125169296170811392, 0
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listen;
history;
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OFFSET
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0,4
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COMMENTS
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Normally these zeros would be omitted in an OEIS entry, but in view of its importance this is included as a pointer to the main entry A000182.
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LINKS
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EXAMPLE
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tan(x) = x + (1/3)*x^3 + (2/15)*x^5 + (17/315)*x^7 + (62/2835)*x^9 + (1382/155925)*x^11 + (21844/6081075)*x^13 + (929569/638512875)*x^15 + ... = x + 2*x^3/3! + 16*x^5/5! + 272*x^7/7! + ...
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MAPLE
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ptan := proc(n) option remember;
if irem(n, 2) = 0 then 0 else
-add(`if`(k=0, 1, binomial(n, k)*ptan(n - k)), k = 0..n, 2) fi end:
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PROG
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(Python)
from functools import cache
from math import comb as binomial
@cache
def ptan(n):
return (0 if n % 2 == 0 else
-sum(binomial(n, k)*ptan(n-k) if k > 0 else 1 for k in range(0, n+1, 2)))
t = ptan(n)
return -t if t < 0 else t
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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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