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A181070 G.f.: A(x) = exp( Sum_{n>=1} (Sum_{k=0..n} C(n,k)^(k+1)*x^k)*x^n/n ). 6
1, 1, 2, 4, 8, 23, 88, 379, 3044, 32116, 379279, 9160509, 237458908, 7651718328, 495105710770, 29747390685988, 2718143583980173, 436044028162542425, 61494671526637653928, 16346049663440380567782, 6106008029903796482509688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjecture: this sequence consists entirely of integers.

Note that the following g.f. does NOT yield an integer series:

exp( Sum_{n>=1} (Sum_{k=0..n} C(n,k)^k * x^k) * x^n/n ).

LINKS

Table of n, a(n) for n=0..20.

EXAMPLE

G.f. A(x) = 1 + x + 2*x^2 + 4*x^3 + 8*x^4 + 23*x^5 + 88*x^6 + ...

The logarithm of g.f. A(x) begins:

log(A(x)) = x + 3*x^2/2 + 7*x^3/3 + 15*x^4/4 + 66*x^5/5 + 357*x^6/6 + 1891*x^7/7 + ... + A181071(n)*x^n/n + ...

and equals the series:

log(A(x)) = (1 + x)*x + (1 + 2^2*x + x^2)*x^2/2

+ (1+ 3^2*x + 3^3*x^2 + x^3)*x^3/3

+ (1+ 4^2*x + 6^3*x^2 + 4^4*x^3 + x^4)*x^4/4

+ (1+ 5^2*x + 10^3*x^2 + 10^4*x^3 + 5^5*x^4 + x^5)*x^5/5

+ (1+ 6^2*x + 15^3*x^2 + 20^4*x^3 + 15^5*x^4 + 6^6*x^5 + x^6)*x^6/6 + ...

PROG

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

CROSSREFS

Cf. A181071(log), variants: A181080, A181072, A181074.

Sequence in context: A151380 A295419 A290816 * A226659 A009327 A027168

Adjacent sequences:  A181067 A181068 A181069 * A181071 A181072 A181073

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 02 2010

STATUS

approved

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Last modified July 17 16:58 EDT 2019. Contains 325107 sequences. (Running on oeis4.)