|
| |
|
|
A284860
|
|
Alternating row sums of the Sheffer triangle (exp(x), exp(3*x) - 1) given in A282629.
|
|
2
|
|
|
|
1, -2, -5, 19, 178, 175, -7739, -72056, -33179, 6899311, 87861076, 215532301, -11151014291, -222077806202, -1563185592617, 22953386817343, 878911293113026, 12330887396253691, 1416506544326449, -4284948239134152536
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
See A282629 for details. This is a generalization of A000587.
|
|
|
LINKS
|
Table of n, a(n) for n=0..19.
|
|
|
FORMULA
|
a(n) = Sum_{m=0..n} (-1)^m*A282629(n, m), n >= 0.
E.g.f.: exp(x)*exp(1 - exp(3*x)).
a(n) = (1/e)*Sum_{m>=0} ((-1)^m / m!)*(1 + 3*m)^n, n >= 0, (Dobiński type formula).- Wolfdieter Lang, Apr 10 2017
|
|
|
MATHEMATICA
|
Fold[#2 - #1 &, Reverse@ #] & /@ Table[Sum[Binomial[m, k] (-1)^(k - m) (1 + 3 k)^n/m!, {k, 0, m}], {n, 0, 19}, {m, 0, n}] (* Michael De Vlieger, Apr 08 2017 *)
|
|
|
PROG
|
(PARI) T(n, m) = sum(k=0, m, binomial(m, k) * (-1)^(k - m) * (1 + 3*k)^n/m!);
a(n) = sum(m=0, n, (-1)^m*T(n, m)); \\ Indranil Ghosh, Apr 10 2017
|
|
|
CROSSREFS
|
Cf. A282629, A000110, A284859.
Sequence in context: A198203 A014466 A304981 * A108799 A193674 A085871
Adjacent sequences: A284857 A284858 A284859 * A284861 A284862 A284863
|
|
|
KEYWORD
|
sign,easy
|
|
|
AUTHOR
|
Wolfdieter Lang, Apr 05 2017
|
|
|
STATUS
|
approved
|
| |
|
|
