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A372251
E.g.f. A(x) satisfies A(x) = exp( x * A(x)^2 * (1 + A(x))/2 ).
1
1, 1, 6, 73, 1364, 34586, 1110496, 43207004, 1976199792, 103925934712, 6178846168976, 409847155094840, 30007066358487040, 2403751529017358144, 209131503815967330816, 19637892118783264231936, 1979605910448187576510208, 213226210180592877512104832
OFFSET
0,3
FORMULA
a(n) = 1/2 * Sum_{k=0..n} (n+k/2+1/2)^(n-1) * binomial(n,k).
a(n) ~ sqrt((1 + s)/(4 + 9*s)) * s^(2*n + 1) * (2 + 3*s)^n * n^(n-1) / (2^n * exp(n)), where s = 1.470103625022272111740158699814771551850270522048... is the root of the equation log(s) = (1 + s)/(2 + 3*s). - Vaclav Kotesovec, Apr 24 2024
PROG
(PARI) a(n) = sum(k=0, n, (n+k/2+1/2)^(n-1)*binomial(n, k))/2;
CROSSREFS
Sequence in context: A202557 A041060 A089926 * A135594 A346960 A168603
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 24 2024
STATUS
approved