A371067 E.g.f. satisfies A(x) = 1 + x*exp(x^2*A(x)^2).

1, 1, 0, 6, 48, 180, 2880, 46200, 483840, 9087120, 203212800, 3752511840, 89413632000, 2510276408640, 66301996400640, 1982685238934400, 67064515854336000, 2274167610024710400, 82881756045036748800, 3301346557970183923200, 135363022243685203968000

Offset

0,4

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = n! * Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(2*k+1,n-2*k)/( (2*k+1)*k! ).

a(n) ~ n^(n-1) / (sqrt(2) * exp(n) * r^(n+1)), where r = 0.450347181930267755599214125867779338412791581819135528888185619948594... and s = 2.1478259175343697310213089706837271102656629945040966643073615920885... are roots of the system of equations exp(r^2*s^2)*r = s-1, 2*(s-1)*r^2*s = 1. - Vaclav Kotesovec, Mar 10 2024

Prog

(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k)^k*binomial(2*k+1, n-2*k)/((2*k+1)*k!));

Crossrefs

Cf. A365283, A370927.

Cf. A161631, A371068.

Sequence in context: A005353 A047927 A059238 * A254832 A026695 A208536

Adjacent sequences: A371064 A371065 A371066 * A371068 A371069 A371070

Keyword

nonn

Author

Seiichi Manyama, Mar 09 2024

Status

approved