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A372160
E.g.f. A(x) satisfies A(x) = exp( 2 * x / (1 - x * A(x)^(1/2)) ).
1
1, 2, 8, 56, 568, 7592, 126364, 2522060, 58760272, 1566368432, 47036927284, 1571615915828, 57841636573912, 2325362549256008, 101399801919677356, 4767244262108645948, 240395075369097851296, 12943276401835227578720, 741127491503124866498404
OFFSET
0,2
FORMULA
E.g.f.: A(x) = B(x)^2 where B(x) is the e.g.f. of A161630.
If e.g.f. satisfies A(x) = exp( r*x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s ), then a(n) = r * n! * Sum_{k=0..n} (t*k+u*(n-k)+r)^(k-1) * binomial(n+(s-1)*k-1,n-k)/k!.
PROG
(PARI) a(n, r=2, s=1, t=0, u=1) = r*n!*sum(k=0, n, (t*k+u*(n-k)+r)^(k-1)*binomial(n+(s-1)*k-1, n-k)/k!);
CROSSREFS
Cf. A161630.
Sequence in context: A181939 A124212 A326009 * A349562 A325290 A197949
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 20 2024
STATUS
approved