STATUS
reviewed
approved
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reviewed
approved
proposed
reviewed
editing
proposed
From Amiram Eldar, Jun 25 2022: (Start)
Sum_{n>=0} 1/a(n) = (BesselI(0, 2*sqrt(2)) - 1)/2.
Sum_{n>=0} (-1)^n/a(n) = (1 - BesselJ(0, 2*sqrt(2)))/2. (End)
a(n) = (n+1)!^2/2^n.
1, 2, 9, 72, 900, 16200, 396900, 12700800, 514382400, 25719120000, 1556006760000, 112032486720000, 9466745127840000, 927741022528320000, 104370865034436000000, 13359470724407808000000, 1930443519676928256000000, 312731850187662377472000000
Self-convolution of A184359.
Self-convolution of A184359.
G.f.: A(x) = 1 + 2*x + 9*x^2 + 72*x^3 + 900*x^4 + 16200*x^5 +...
a[n_] := (n + 1)!^2/2^n; Array[a, 20, 0] (* Amiram Eldar, Jun 25 2022 *)
(PARI) {a(n)=(n+1)!^2/2^n}
approved
editing
_Paul D. Hanna (pauldhanna(AT)juno.com), _, Jan 16 2011
reviewed
approved
proposed
reviewed
allocated for Paul D. Hanna
a(n) = (n+1)!^2/2^n.
1, 2, 9, 72, 900, 16200, 396900, 12700800, 514382400, 25719120000, 1556006760000, 112032486720000, 9466745127840000, 927741022528320000, 104370865034436000000, 13359470724407808000000, 1930443519676928256000000
0,2
Self-convolution of A184359.
G.f.: A(x) = 1 + 2*x + 9*x^2 + 72*x^3 + 900*x^4 + 16200*x^5 +...
A(x)^(1/2) = 1 + x + 4*x^2 + 32*x^3 + 410*x^4 + 7562*x^5 + 188736*x^6 +...+ A184359(n)*x^n +...
(PARI) {a(n)=(n+1)!^2/2^n}
allocated
nonn
Paul D. Hanna (pauldhanna(AT)juno.com), Jan 16 2011
approved
proposed
allocated for Paul D. Hanna
allocated
approved