|
Search: id:A138736
|
|
| |
|
| 1, 1, 4, 36, 368, 5200, 90432, 1884736, 45817088, 1273874688, 39891461120, 1389816423424, 53334303584256, 2235679577657344, 101651458028158976, 4983219643056537600, 262026143585449607168, 14711289584591513387008
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
The n-th term of the n-th inverse binomial transform of A138737 equals (n+1)^(n-1) for n>=0.
Related to LambertW(-x)/(-x) = Sum_{n>=0} (n+1)^(n-1)*x^n/n!.
|
|
FORMULA
|
O.g.f. satisfies: [x^n] A( x/(1+(n-1)*x) )/(1+(n-1)*x) = (n+1)^(n-1) for n>=0.
E.g.f. satisfies: [x^n] A(x)*exp(-(n-1)*x) = (n+1)^(n-1)/n! for n>=0.
|
|
PROGRAM
|
(PARI) {a(n)=local(A=[1]); for(k=1, n, A=concat(A, 0); A[k+1]=(k+1)^(k-1)-Vec(subst(Ser(A), x, x/(1+(k-1)*x+x*O(x^k)))/(1+(k-1)*x))[k+1]); A[n+1]}
|
|
CROSSREFS
|
Cf. A138737.
Adjacent sequences: A138733 A138734 A138735 this_sequence A138737 A138738 A138739
Sequence in context: A000765 A026334 A163455 this_sequence A019999 A002894 A131765
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul D. Hanna (pauldhanna(AT)juno.com), Apr 05 2008
|
|
|
Search completed in 0.002 seconds
|
