A367372 Expansion of the e.g.f. (exp(x) / (4 - 3*exp(x)))^(1/2).

1, 2, 10, 86, 1042, 16262, 310450, 7007366, 182550322, 5390680262, 177934787890, 6492033136646, 259439670455602, 11270026085032262, 528753577418113330, 26645797408814241926, 1435417112274224920882, 82316745016710520696262

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * (Product_{j=0..k-1} (4*j+2)) * Stirling2(n,k) = Sum_{k=0..n} (-1)^(n-k) * (2*k)! * Stirling2(n,k)/k!.

a(0) = 1; a(n) = Sum_{k=1..n} (-1)^k * (2*k/n - 4) * binomial(n,k) * a(n-k).

a(0) = 1; a(n) = 2*a(n-1) + 3*Sum_{k=1..n-1} binomial(n-1,k) * a(n-k).

Prog

(PARI) a(n) = sum(k=0, n, (-1)^(n-k)*prod(j=0, k-1, 4*j+2)*stirling(n, k, 2));

Crossrefs

Cf. A136728, A201354, A367373.

Cf. A001813, A354242.

Sequence in context: A132397 A202745 A364396 * A372177 A371005 A208833

Adjacent sequences: A367369 A367370 A367371 * A367373 A367374 A367375

Keyword

nonn

Author

Seiichi Manyama, Nov 15 2023

Status

approved