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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

Table of n, a(n) for n=0..17.

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

Cf. A230323, A125282, A218683.

Sequence in context: A214933 A230323 A217251 * A086371 A229954 A228513

Adjacent sequences:  A125278 A125279 A125280 * A125282 A125283 A125284

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 29 2006, Sep 22 2007

STATUS

approved

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Last modified September 20 10:51 EDT 2021. Contains 347584 sequences. (Running on oeis4.)