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A181084 G.f.: exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^(n+k+1) * x^k] * x^n/n ). 2
1, 1, 2, 10, 92, 1367, 87090, 20385333, 6633475836, 4096297538926, 14834973644512627, 119919823546238898903, 1273371038284317852447990, 41086272137585936052959008420, 6982122140549374036504235218052104 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Conjecture: this sequence consists entirely of integers.

LINKS

Table of n, a(n) for n=0..14.

EXAMPLE

G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 92*x^4 + 1367*x^5 + 87090*x^6 +...

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

log(A(x)) = x + 3*x^2/2 + 25*x^3/3 + 327*x^4/4 + 6336*x^5/5 + 513657*x^6/6 +...+ A181085(n)*x^n/n +...

and equals the series:

log(A(x)) = (1 + x)*x + (1 + 2^4*x + x^2)*x^2/2

+ (1+ 3^5*x + 3^6*x^2 + x^3)*x^3/3

+ (1+ 4^6*x + 6^7*x^2 + 4^8*x^3 + x^4)*x^4/4

+ (1+ 5^7*x + 10^8*x^2 + 10^9*x^3 + 5^10*x^4 + x^5)*x^5/5

+ (1+ 6^8*x + 15^9*x^2 + 20^10*x^3 + 15^11*x^4 + 6^12*x^5 + x^6)*x^6/6 +...

PROG

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

CROSSREFS

Cf. A181085 (log), variants: A181082, A181080.

Sequence in context: A289020 A195415 A336271 * A063385 A293709 A063393

Adjacent sequences:  A181081 A181082 A181083 * A181085 A181086 A181087

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 28 2010

STATUS

approved

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Last modified August 7 23:38 EDT 2020. Contains 336279 sequences. (Running on oeis4.)