A350972 - OEIS

%I #17 Jun 06 2022 06:10:35

%S 0,1,0,2,0,16,0,272,0,7936,0,353792,0,22368256,0,1903757312,0,

%T 209865342976,0,29088885112832,0,4951498053124096,0,

%U 1015423886506852352,0,246921480190207983616,0,70251601603943959887872,0,23119184187809597841473536,0,8713962757125169296170811392,0

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

%C 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.

%e 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! + ...

%p ptan := proc(n) option remember;

%p     if irem(n, 2) = 0 then 0 else

%p     -add(`if`(k=0, 1, binomial(n, k)*ptan(n - k)), k = 0..n,2) fi end:

%p A350972 := n -> abs(ptan(n)): seq(A350972(n), n=0..29); # _Peter Luschny_, Jun 06 2022

%o (Python)

%o from functools import cache

%o from math import comb as binomial

%o @cache

%o def ptan(n):

%o     return (0 if n % 2 == 0 else

%o     -sum(binomial(n,k)*ptan(n-k) if k > 0 else 1 for k in range(0,n+1,2)))

%o def A350972(n):

%o     t = ptan(n)

%o     return -t if t < 0 else t

%o print([A350972(n) for n in range(99)]) # _Peter Luschny_, Jun 06 2022

%Y Cf. A000182, A000364, A122045.

%Y See also A009006, A155585.

%K nonn

%O 0,4

%A _N. J. A. Sloane_, Mar 05 2022