|
| |
|
|
A125281
|
|
E.g.f. satisfies: A(x) = Sum{n>=0} x^n * A(n*x)/n!.
|
|
4
| |
|
|
1, 1, 3, 16, 149, 2316, 59047, 2429554, 159549945, 16557985432, 2693862309131, 682199144788734, 267277518618047797, 161130714885281760100, 148762112860064623199295, 209444428223095096806228346
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
FORMULA
| a(n) = Sum_{k=0..n-1} C(n,k)*(n-k)^k * a(k) for n>0 with a(0)=1.
|
|
|
EXAMPLE
| A(x) = 1 + x + 3*x^2/2! + 16*x^3/3! + 149*x^4/4! + 2316*x^5/5! +...
E.g.f. A(x) satisfies: A(x) = 1 + x*A(x) + x^2*A(2x)/2! + x^3*A(3x)/3! + x^4*A(4x)/4! +...
which leads to the recurrence illustrated by:
a(3) = 1*3^0*(1) + 3*2^1*(1) + 3*1^2*(3) = 16;
a(4) = 1*4^0*(1) + 4*3^1*(1) + 6*2^2*(3) + 4*1^3*(16) = 149;
a(5) = 1*5^0*(1) + 5*4^1*(1) + 10*3^2*(3) + 10*2^3*(16) + 5*1^4*(149) = 2316.
|
|
|
PROG
| (PARI) {a(n)=if(n==0, 1, sum(k=0, n-1, binomial(n, k)*(n-k)^k*a(k)))}
|
|
|
CROSSREFS
| Cf. A125282 (variant).
Sequence in context: A109398 A006058 A121588 * A086371 A135753 A191959
Adjacent sequences: A125278 A125279 A125280 * A125282 A125283 A125284
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Nov 29 2006, Sep 22 2007
|
| |
|
|
