|
|
A227094
|
|
Binomial transform of A013999.
|
|
0
|
|
|
1, 2, 5, 18, 91, 574, 4199, 34650, 318645, 3237034, 36041657, 436713506, 5722676895, 80654047942, 1216703923147, 19562850695690, 333991034593833, 6034449711055890, 115036771019660269, 2307582082535387570, 48588759062255598563, 1071533741191907032590
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = sum(C(n,k)*A013999(k), k=0..n).
G.f.: sum(k!*x^(k-1)*(1-2*x)^k/(1-x)^(2*k), k>=1).
|
|
MAPLE
|
a:= proc(n) option remember; `if`(n<4, [1, 2, 5, 18][n+1],
(n+6)*a(n-1)-(5*n+7)*a(n-2)+(8*n-7)*a(n-3)-(4*n-12)*a(n-4))
end:
|
|
MATHEMATICA
|
a[n_] := a[n] = If[n < 4, {1, 2, 5, 18}[[n + 1]], (n + 6)*a[n - 1] - (5*n + 7)*a[n - 2] + (8*n - 7)*a[n - 3] - (4*n - 12)*a[n - 4]];
|
|
PROG
|
(Maxima) f(n):=sum(binomial(n-k+1, k)*(-1)^k*(n-k+1)!, k, 0, floor((n+1)/2)); a(n):=sum(binomial(n, k)*f(k), k, 0, n); makelist(a(n), n, 0, 20);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|