A351937 Expansion of e.g.f. exp( (sinh(x) + x*cosh(x)) / 2 ).

1, 1, 1, 3, 9, 24, 99, 418, 1769, 9320, 49541, 278912, 1764825, 11319784, 77850287, 570610472, 4290387409, 34316005632, 285335249065, 2455224885440, 22165590003849, 206191758121856, 1989511661589435, 19903718061574144, 204795484665487865, 2179948112062667392

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..568

Formula

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

Mathematica

nmax = 25; CoefficientList[Series[Exp[(Sinh[x] + x Cosh[x])/2], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, 2 k] (k + 1) a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 25}]

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace(exp((sinh(x) + x*cosh(x))/2))) \\ Michel Marcus, Feb 26 2022

Crossrefs

Cf. A000248, A003724, A003727, A349103, A349105.

Sequence in context: A290511 A103301 A148920 * A204448 A380050 A032681

Adjacent sequences: A351934 A351935 A351936 * A351938 A351939 A351940

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 26 2022

Status

approved