A377740 E.g.f. satisfies A(x) = exp(x) * (1 + x * A(x))^2.

1, 3, 19, 199, 2957, 57341, 1377175, 39531927, 1321803705, 50491876825, 2170432191491, 103726081148339, 5456983990544773, 313449393386822421, 19521567325327386831, 1310428405901227674511, 94325931842372734994417, 7248016420075574268626225, 592190617414334419733622139

Offset

0,2

Links

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

Formula

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

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

a(n) = A295238(n+1)/(n+1).

Prog

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

Crossrefs

Cf. A072597, A377741.

Cf. A295238, A377574.

Sequence in context: A007151 A269787 A303927 * A288693 A195895 A127502

Adjacent sequences: A377737 A377738 A377739 * A377741 A377742 A377743

Keyword

nonn

Author

Seiichi Manyama, Nov 05 2024

Status

approved