A335644 Expansion of e.g.f. Product_{k>0} (1 + sin(x)^k / k!).

1, 1, 1, 3, 1, -23, -2, -28, -2435, 253, 118966, 158400, -5277106, -6453094, 377003877, 150562341, -38919169331, -49489639843, 4097920244054, 15989402021656, -397866849121614, -3949517739363706, 34992745696351023, 937723673130987379, -2417716098650478930, -223227071403982903362

Offset

0,4

Links

Table of n, a(n) for n=0..25.

Formula

E.g.f.: exp( Sum_{i>0} Sum_{j>0} (-1)^(i+1)*sin(x)^(i*j)/(i*(j!)^i) ).

Mathematica

max = 25; Range[0, max]! * CoefficientList[Series[Product[1 + Sin[x]^k/k!, {k, 1, max}], {x, 0, max}], x] (* Amiram Eldar, Oct 04 2020 *)

Prog

(PARI) N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, 1+sin(x)^k/k!)))
(PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(i=1, N, sum(j=1, N\i, (-1)^(i+1)*sin(x)^(i*j)/(i*j!^i))))))

Crossrefs

Cf. A007837, A335629, A335637, A335642, A336046.

Sequence in context: A010291 A370948 A306619 * A027477 A260780 A243769

Adjacent sequences: A335641 A335642 A335643 * A335645 A335646 A335647

Keyword

sign

Author

Seiichi Manyama, Oct 03 2020

Status

approved