A355157 E.g.f.: exp(-x*tan(x)/2).

1, -1, -1, -3, 81, 5815, 367791, 26531589, 2231306849, 213451322031, 21883750567455, 2048495154903373, 38238322254619953, -84508521173113956633, -48971496478118456699569, -23204642085706390327411755, -10849535606183313563987736639, -5259600981361065001871911307681, -2687430634156750207499977165012161

Offset: 0

Author

Paul D. Hanna, Jun 21 2022

Keywords

• sign

Examples

			E.g.f. A(x) = 1 - x^2/2! - x^4/4! - 3*x^6/6! + 81*x^8/8! + 5815*x^10/10! + 367791*x^12/12! + 26531589*x^14/14! + 2231306849*x^16/16! + 213451322031*x^18/18! + 21883750567455*x^20/20! + 2048495154903373*x^22/22! + 38238322254619953*x^24/24! - 84508521173113956633*x^26/26! + ...
The signs (+/-) of the terms a(n) begin:
[+,
-,-,-,
+,+,+,+,+,+,+,+,+,
-,-,-,-,-,-,-,-,-,-,-,-,-,
+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,
-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,-,
+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,+,
-, ...].
The change in signs take place at positions:
[1, 4, 13, 26, 45, 68, 97, 130, 168, 211, 259, 312, 370, 433, 501, 574, 652, 734, 822, 914, 1012, 1114, 1222, 1334, 1451, 1573, 1700, 1832, 1969, 2111, 2258, 2410, 2566, 2728, 2895, ...].
		

Crossrefs

Cf. A354245, A009273.

Programs

PARI

{a(n) = my(A = exp(-x * tan(x +O(x^(2*n+1)))/2) ); (2*n)!*polcoeff(A,2*n)}
for(n=0,20,print1(a(n),", "))