|
|
A367155
|
|
E.g.f. satisfies A(x) = 1 + A(x)^3 * log(1 + x).
|
|
4
|
|
|
1, 1, 5, 56, 948, 21804, 634284, 22348584, 925322784, 44039346264, 2369167375656, 142173632632272, 9416315321258928, 682290228636729504, 53689645309437175968, 4559660591348115191808, 415683140400707316145920, 40490500091575002629253120
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} (3*k)!/(2*k+1)! * Stirling1(n,k).
a(n) ~ 9 * n^(n-1) / (2^(5/2) * (exp(4/27) - 1)^(n - 1/2) * exp(n + 2/27)). - Vaclav Kotesovec, Nov 10 2023
|
|
MATHEMATICA
|
Table[Sum[(3*k)!/(2*k+1)! * StirlingS1[n, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 10 2023 *)
|
|
PROG
|
(PARI) a(n) = sum(k=0, n, (3*k)!/(2*k+1)!*stirling(n, k, 1));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|