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A167007 G.f.: A(x) = exp( Sum_{n>=1} A167010(n)*x^n/n ) where A167010(n) = Sum_{k=0..n} binomial(n,k)^n. 2
1, 2, 5, 26, 501, 42262, 14564184, 18926665052, 96371663657380, 1825266130738144920, 136764680697906838980633, 38133043109557952095731186822, 42464330390232136488003531922964743 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..12.

FORMULA

a(n) = (1/n)*Sum_{k=1..n} A167010(k)*a(n-k) for n>0 with a(0)=1. - Paul D. Hanna, Nov 25 2009

EXAMPLE

G.f.: A(x) = 1 + 2*x + 5*x^2 + 26*x^3 + 501*x^4 + 42262*x^5 + ...

log(A(x)) = 2*x + 6*x^2/2 + 56*x^3/3 + 1810*x^4/4 + 206252*x^5/5 + 86874564*x^6/6 + ... + A167010(n)*x^n/n + ...

PROG

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^m)*x^m/m)+x*O(x^n)), n)}

(PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, sum(j=0, k, binomial(k, j)^k)*a(n-k)))} \\ Paul D. Hanna, Nov 25 2009

CROSSREFS

Cf. A167010, A155200, A167006.

Sequence in context: A323293 A258868 A322705 * A064006 A003095 A023362

Adjacent sequences:  A167004 A167005 A167006 * A167008 A167009 A167010

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 17 2009

STATUS

approved

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Last modified June 4 08:18 EDT 2020. Contains 334825 sequences. (Running on oeis4.)