A394728 Expansion of e.g.f. exp( sqrt(1-x^2) - 1 + x*arcsin(x) ) (even powers only).

1, 1, 4, 39, 827, 34380, 2473197, 275864757, 44025149100, 9497957945859, 2658392388727335, 935814016563467580, 404396026663235193369, 210377008332888349156425, 129655968695522299896282900, 93400142845800651895616978655, 77748684005223840073739923036755

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n-1,2*k-1) * A001818(k-1) * a(n-k).

E.g.f. A(x) satisfies A'(x)/A(x) = arcsin(x).

Example

E.g.f.: 1 + x^2/2! + 4*x^4/4! + 39*x^6/6! + 827*x^8/8! + 34380*x^10/10! + ...

Crossrefs

Cf. A001147, A001818, A394727.

Sequence in context: A299426 A188418 A136653 * A165434 A348118 A341473

Adjacent sequences: A394725 A394726 A394727 * A394729 A394730 A394731

Keyword

nonn

Author

Seiichi Manyama, Mar 30 2026

Status

approved