[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A365031
E.g.f. satisfies A(x) = exp(x * A(x) * (1 + x * A(x))^2).
3
1, 1, 7, 70, 1085, 22176, 569107, 17583616, 636085305, 26383168000, 1234691104031, 64368785424384, 3699873561469813, 232476344504965120, 15853643565560296875, 1166213594266747273216, 92052000392983157418353, 7760655405804462332903424
OFFSET
0,3
FORMULA
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*k,n-k)/k!.
E.g.f.: (1/x) * Series_Reversion( x*exp(-x*(1 + x)^2) ). - Seiichi Manyama, Sep 23 2024
MATHEMATICA
Array[#!*Sum[ (# + 1)^(k - 1)*Binomial[2 k, # - k]/k!, {k, 0, #}] &, 18, 0] (* Michael De Vlieger, Aug 18 2023 *)
PROG
(PARI) a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(2*k, n-k)/k!);
CROSSREFS
Cf. A364939.
Sequence in context: A051604 A346668 A362775 * A097630 A090647 A200929
KEYWORD
nonn,changed
AUTHOR
Seiichi Manyama, Aug 17 2023
STATUS
approved