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 A364938 E.g.f. satisfies A(x) = exp( x / (1 - x*A(x))^3 ). 3
 1, 1, 7, 73, 1141, 23821, 623341, 19650793, 725478601, 30714824377, 1467394945561, 78103975313101, 4583805610661245, 294093243091237669, 20479664124384110101, 1538423857251845781841, 124007828871708989798161, 10676865465119963987425009 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..17. FORMULA a(n) = n! * Sum_{k=0..n} (n-k+1)^(k-1) * binomial(n+2*k-1,n-k)/k!. a(n) ~ sqrt(s*(1 + 2*r*s) / (4 + 3*r - 12*r*s + 12*r^2*s^2 - 4*r^3*s^3)) * n^(n-1) / (exp(n) * r^n), where r = 0.1811100305436879929789759231994897963241226689... and s = 1.893740207738561813713992833266450862854198944672... are real roots of the system of equations exp(r/(1 - r*s)^3) = s, 3*s*r^2 = (1 - r*s)^4. - Vaclav Kotesovec, Nov 18 2023 MATHEMATICA Join[{1}, Table[n! * Sum[(n-k+1)^(k-1) * Binomial[n+2*k-1, n-k]/k!, {k, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Nov 18 2023 *) PROG (PARI) a(n) = n!*sum(k=0, n, (n-k+1)^(k-1)*binomial(n+2*k-1, n-k)/k!); CROSSREFS Cf. A161630, A161635. Cf. A364940, A364942, A364981. Sequence in context: A325930 A360544 A352123 * A134281 A360934 A215612 Adjacent sequences: A364935 A364936 A364937 * A364939 A364940 A364941 KEYWORD nonn AUTHOR Seiichi Manyama, Aug 14 2023 STATUS approved

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Last modified June 13 00:51 EDT 2024. Contains 373362 sequences. (Running on oeis4.)