A350972 - OEIS

A350972

E.g.f. = tan(x).

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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OFFSET

0,4

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..32.

EXAMPLE

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! + ...

MAPLE

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:

A350972 := n -> abs(ptan(n)): seq(A350972(n), n=0..29); # Peter Luschny, Jun 06 2022

PROG

(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)))

def A350972(n):

t = ptan(n)

return -t if t < 0 else t

print([A350972(n) for n in range(99)]) # Peter Luschny, Jun 06 2022

CROSSREFS

Cf. A000182, A000364, A122045.