Sequence Sage

$\text{Sage}(n)=\frac{2^{2^n}}{2^{n+1}}=2^{(2^n-n-1)}$ Template:Spaces $\text{DubSage}(n)=\frac{2^{2^n}}{2^n}=2^{(2^n-n)}$

Sequences Sage_(Drop)

	0	1	2	3	4	5	6	7
Eulerian numbers (Template:Oeis)	0	0	1	4	11	26	57	120
🌊 Sage (~Template:Oeis)	1	1	2	16	2048	67108864	144115188075855872	1329227995784915872903807060280344576
💧 SageDrop	1	0	1	14	2032	67106816	144115188008747008	1329227995784915872759691872204488704

a ↦ sharp families

Sage(a) SageDrop(a)

is the number of Template:Boolf-prop Template:Boolf-prop with

Template:Boolf-prop Template:Boolf-prop

a.

Template:AnchorSequences DubSage_(Drop)

	0	1	2	3	4	5	6	7
🌊 DubSage	2	2	4	32	4096	134217728	288230376151711744	2658455991569831745807614120560689152
💧 DubSageDrop	2	0	2	28	4064	134213632	288230376017494016	2658455991569831745519383744408977408

a ↦ extroverted families

DubSage(a) DubSageDrop(a)

is the number of Template:Boolf-prop Template:Boolf-prop with

Template:Boolf-prop Template:Boolf-prop

a.

Template:AnchorSequences TornSage_(Drop)

$\text{for}n\ge 2:\text{TornSage}(n)=\frac{\text{Sage}(n)}{2}$

	1	2	3	4	5	6	7
🌊 TornSage (~Template:Oeis)	1	1	8	1024	33554432	72057594037927936	664613997892457936451903530140172288
💧 TornSageDrop	1	0	7	1016	33553408	72057594004373504	664613997892457936379845936102244352

a ↦ sharp super-families

TornSage(a) TornSageDrop(a)

is the number of Template:Boolf-prop Template:Boolf-prop with

Template:Boolf-prop Template:Boolf-prop

a.

Compare Template:Boolf-seq.