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

Offset: 0

Author

N. J. A. Sloane, Mar 05 2022

Keywords

• nonn

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.

Examples

			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! + ...
		

Crossrefs

Cf. A000182, A000364, A122045.

See also A009006, A009764, A155585.

Programs

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

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