A250916 E.g.f.: exp(C(x)^2 - 1) where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers, A000108.

1, 2, 14, 152, 2236, 41512, 930904, 24474368, 738241424, 25132379552, 953267419744, 39867845243008, 1822779782497216, 90453927667906688, 4842249786763758464, 278167945047964156928, 17069371221016503644416, 1114374972408995525243392, 77126208846034435924819456

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: exp( (1-2*x-2*x^2 - sqrt(1-4*x))/(2*x^2) ).

a(n) ~ 2^(2*n+5/2) * n^(n-1) / exp(n-3). - Vaclav Kotesovec, Aug 22 2017

Example

E.g.f.: A(x) = 1 + 2*x + 14*x^2/2! + 152*x^3/3! + 2236*x^4/4! + 41512*x^5/5! +...
such that log(A(x)) = C(x)^2 - 1,
log(A(x)) = 2*x + 5*x^2 + 14*x^3 + 42*x^4 + 132*x^5 + 429*x^6 + 1430*x^7 +...
where C(x) = 1 + x*C(x)^2 is the g.f. of A000108.

Prog

(PARI) {a(n)=local(C=1); for(i=0, n, C=1+x*C^2 +x*O(x^n)); n!*polcoeff(exp(C^2-1), n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n) = n!*polcoeff(exp((1-2*x - sqrt(1-4*x + x^3*O(x^n)))/(2*x^2) - 1), n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A251568, A250917, A000108.

Sequence in context: A087132 A036079 A121227 * A354751 A211398 A219430

Adjacent sequences: A250913 A250914 A250915 * A250917 A250918 A250919

Keyword

nonn

Author

Paul D. Hanna, Dec 06 2014

Status

approved