|
| |
|
|
A187665
|
|
Binomial convolution of the central Lah numbers and the central Stirling numbers of the second kind.
|
|
1
|
|
|
|
1, 3, 47, 1440, 67533, 4280175, 341307292, 32750424588, 3670267277749, 470237282353989, 67781221867781615, 10855095004543985756, 1912103925425230231884, 367398970712627913234708, 76469792506315229551855080
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
Table of n, a(n) for n=0..14.
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} binomial(n,k)*A187535(k)* A048993(2n-2k,n-k).
a(n) ~ c * 16^n * (n-1)!, where c = 0.172113078600558193773... - Vaclav Kotesovec, Jul 05 2021
|
|
|
MAPLE
|
A048993 := proc(n, k) combinat[stirling2](n, k) ; end proc:
A187535 := proc(n) if n=0 then 1 else binomial(2*n-1, n-1)*(2*n)!/n! end if; end proc:
A187665 := proc(n) add(binomial(n, k)*A187535(k)*A048993(2*n-2*k, n-k), k=0..n) ; end proc:
seq(A187665(n), n=0..10) ; # R. J. Mathar, Mar 28 2011
|
|
|
MATHEMATICA
|
L[n_] := If[n == 0, 1, Binomial[2n - 1, n - 1](2n)!/n!]
Table[Sum[Binomial[n, k]L[k]StirlingS2[2n - 2k, n - k], {k, 0, n}], {n, 0, 14}]
|
|
|
PROG
|
(Maxima) L(n):= if n=0 then 1 else binomial(2*n-1, n-1)*(2*n)!/n!;
makelist(sum(binomial(n, k)*L(k)*stirling2(2*n-2*k, n-k), k, 0, n), n, 0, 12);
|
|
|
CROSSREFS
|
Sequence in context: A197203 A197801 A239450 * A088718 A219162 A016548
Adjacent sequences: A187662 A187663 A187664 * A187666 A187667 A187668
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Emanuele Munarini, Mar 12 2011
|
|
|
STATUS
|
approved
|
| |
|
|
