|
| |
|
|
A158690
|
|
Expansion of the basic hypergeometric series 1 + (1-exp(-t)) + (1-exp(-t))*(1-exp(-3t)) + (1-exp(-t))*(1-exp(-3t))*(1-exp(-5t)) + ... as a series in t.
|
|
5
| |
|
|
1, 1, 5, 55, 1073, 32671, 1431665, 85363615, 6646603073, 654896692351, 79656194515025, 11722538113191775, 2052949879753739873, 421931472111868912831, 100568330857984368195185
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| We appear to get the same sequence by expanding 1 - (1-exp(t)) + (1-exp(t))*(1-exp(2t)) - (1-exp(t))*(1-exp(2t))*(1-exp(3t)) + ... as a series in t. Compare with A079144. For other sequences with generating functions of a similar type see A000364, A000464, A002105 and A002439.
|
|
|
FORMULA
| Basic hypergeometric generating function: 1 + Sum {n = 1..inf} Product {k = 1..n} (1-exp(2*k-1)*t)) = 1 + t + 5*t^2/2! + 55*t^3/3! + ....
|
|
|
CROSSREFS
| A000364, A000464, A002105, A002439, A079144, A158691.
Sequence in context: A130031 A119399 A177557 * A192723 A102221 A056600
Adjacent sequences: A158687 A158688 A158689 * A158691 A158692 A158693
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Peter Bala (pbala(AT)talktalk.net), Mar 24 2009
|
| |
|
|
