A352429 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/4)} binomial(n,4*k+1) * a(n-4*k-1).

1, 1, 2, 6, 24, 121, 732, 5166, 41664, 378001, 3810512, 42253926, 511139904, 6698457481, 94535404992, 1429477706286, 23056267551744, 395120495014561, 7169579673404672, 137321623511274246, 2768602189953629184, 58609968225266985241, 1299827736206335767552, 30137364376923272989806

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..449

Formula

E.g.f.: 1 / (1 - Sum_{k>=0} x^(4*k+1) / (4*k+1)!).

E.g.f.: 1 / (1 - (sin(x) + sinh(x)) / 2).

Mathematica

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, 4 k + 1] a[n - 4 k - 1], {k, 0, Floor[(n - 1)/4]}]; Table[a[n], {n, 0, 23}]
nmax = 23; CoefficientList[Series[1/(1 - Sum[x^(4 k + 1)/(4 k + 1)!, {k, 0, nmax}]), {x, 0, nmax}], x] Range[0, nmax]!

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\4, x^(4*k+1)/(4*k+1)!)))) \\ Seiichi Manyama, Mar 23 2022

Crossrefs

Cf. A000670, A006154, A243665, A291975, A306347, A352428, A352430.

Sequence in context: A357922 A275753 A349089 * A352437 A144167 A104983

Adjacent sequences: A352426 A352427 A352428 * A352430 A352431 A352432

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 16 2022

Status

approved