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A125281 E.g.f. satisfies: A(x) = Sum{n>=0} x^n * A(n*x)/n!. 6
1, 1, 3, 16, 149, 2316, 59047, 2429554, 159549945, 16557985432, 2693862309131, 682199144788734, 267277518618047797, 161130714885281760100, 148762112860064623199295, 209444428223095096806228346, 447998198975235291015396393713, 1450973400598977755884988875863216 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
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! +...
where
A(x) = 1 + x*A(x) + x^2*A(2*x)/2! + x^3*A(3*x)/3! + x^4*A(4*x)/4! + x^5*A(5*x)/5! +...
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)))}
(PARI) {a(n)=local(A=1); for(i=1, n, A=sum(k=0, n, x^k/k!*subst(A, x, k*x)+x*O(x^n))); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
Sequence in context: A214933 A230323 A217251 * A086371 A229954 A228513
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 29 2006, Sep 22 2007
STATUS
approved

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Last modified July 19 17:03 EDT 2024. Contains 374410 sequences. (Running on oeis4.)