A331404 a(0) = 1; a(n) = Sum_{k=1..n} (-1)^(n - k) * binomial(n,k) * a(k-1) * a(n-k).

1, 1, -1, -7, 19, 229, -1009, -17263, 105211, 2332141, -18148681, -494079367, 4678377859, 151026527989, -1684778524129, -62909200846303, 807879476432971, 34252260613710781, -497629527847938361, -23615390533271153527, 382915997208515638099, 20108383384185058286149

Offset

0,4

Comments

Conjecture: the e.g.f. of this sequence is the inverse function of y = x - 1/x - log(x) in a neighborhood of x = 1 on the complex plane, and its convergence radius is sqrt(3) - Pi/3 = 0.6848532563... - Jianing Song, Sep 30 2024

Links

Table of n, a(n) for n=0..21.

Mathematica

a[n_] := a[n] = Sum[(-1)^(n - k) Binomial[n, k] a[k - 1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 21}]

Prog

(PARI) seq(n)={my(a=vector(n+1)); a[1]=1; for(n=1, #a-1, a[1+n]=sum(k=1, n, (-1)^(n - k) * binomial(n, k) * a[k] * a[1+n-k])); a} \\ Andrew Howroyd, Jan 16 2020

Crossrefs

Cf. A000182, A001147, A090192.

Sequence in context: A107195 A201479 A228150 * A191624 A221740 A364572

Adjacent sequences: A331401 A331402 A331403 * A331405 A331406 A331407

Keyword

sign

Author

Ilya Gutkovskiy, Jan 16 2020

Status

approved