A353609 Product_{n>=1} (1 + a(n)*x^(2*n)/(2*n)!) = cosh(x).

1, 1, -14, 393, -14744, 972610, -74928944, 9322093753, -1163849271296, 228519734620776, -44942000161435904, 12717856972091286642, -3539995034294896016384, 1371560847857743301790928, -510461123036204706738612224, 268938575250382935485761673113

Offset: 1

Author

Ilya Gutkovskiy, May 07 2022

Keywords

• sign

Crossrefs

Cf. A006973, A137852, A170912, A170913, A353607, A353608, A353610, A353611.

Programs

Mathematica

nn = 16; f[x_] := Product[(1 + a[n] x^(2 n)/(2 n)!), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Cosh[x], {x, 0, 2 nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten