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A277610 G.f.: 1 / (1 - Sum_{k>=1} k^k * x^k ). 3
1, 1, 5, 36, 339, 3999, 57388, 977577, 19348425, 436886364, 11084633347, 312102694743, 9653262860564, 325242329821529, 11853828646799153, 464582888781914004, 19481645509391087747, 870252961810204549919, 41253445365917239409916, 2068244310629828065675481, 109336176534540098236055769, 6078206718063279979791668252, 354471031348340363987467541507, 21638266052947649126008431859703, 1379839169160669434086676475756260 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Robert Israel, Table of n, a(n) for n = 0..386

FORMULA

G.f.: exp( Sum_{n>=1} [ Sum_{k>=1} k^k * x^k ]^n / n ).

a(n) ~ n^n * (1 + 2*exp(-1)/n). - Vaclav Kotesovec, Nov 06 2016

"INVERT" transform of A000312. - Alois P. Heinz, Sep 22 2017

EXAMPLE

G.f.: A(x) = 1 + x + 5*x^2 + 36*x^3 + 339*x^4 + 3999*x^5 + 57388*x^6 + 977577*x^7 + 19348425*x^8 + 436886364*x^9 + 11084633347*x^10 +...

The logarithm of the g.f. begins:

log(A(x)) = x + 9*x^2/2 + 94*x^3/3 + 1181*x^4/4 + 17681*x^5/5 + 310308*x^6/6 + 6276565*x^7/7 + 144052445*x^8/8 + 3701113150*x^9/9 + 105252411369*x^10/10 + 3281812541569*x^11/11 + 111313031195216*x^12/12 + 4079782609460013*x^13/13 + 160665945152295921*x^14/14 + 6765274535733165854*x^15/15 +...

which equals the sum

log(A(x)) = (x + 4*x^2 + 27*x^3 + 256*x^4  + 3125*x^5 +...) +

(x^2 + 8*x^3 + 70*x^4 + 728*x^5 + 9027*x^6 + 132136*x^7 +...)/2 +

(x^3 + 12*x^4 + 129*x^5 + 1480*x^6 + 19002*x^7 +...)/3 +

(x^4 + 16*x^5 + 204*x^6 + 2576*x^7 + 34602*x^8 +...)/4 +

(x^5 + 20*x^6 + 295*x^7 + 4080*x^8 + 57635*x^9 +...)/5 +

(x^6 + 24*x^7 + 402*x^8 + 6056*x^9 + 90165*x^10 +...)/6 +

(x^7 + 28*x^8 + 525*x^9 + 8568*x^10 + 134512*x^11 +...)/7 +

... +

(x + 2^2*x^2 + 3^3*x^3 + 4^4*x^4 + 5^5*x^5 +...+ k^k*x^k +...)^n/n +

...

MAPLE

G:= 1/(1-Sum(k^k*x^k, k=1..infinity)):

S:= series(G, x, 51):

seq(coeff(S, x, j), j=0..50); # Robert Israel, Nov 06 2016

# second Maple program:

a:= proc(n) option remember; `if`(n=0, 1,

      add(j^j*a(n-j), j=1..n))

    end:

seq(a(n), n=0..20);  # Alois P. Heinz, Sep 22 2017

MATHEMATICA

CoefficientList[Series[1/(1 - Sum[k^k * x^k, {k, 1, 20}]), {x, 0, 20}], x] (* Vaclav Kotesovec, Nov 06 2016 *)

PROG

(PARI) {a(n) = polcoeff( 1/(1 - sum(k=1, n+1, k^k * x^k +x*O(x^n)) ), n)}

for(n=0, 30, print1(a(n), ", "))

CROSSREFS

Cf. A000312, A088342, A277611.

Sequence in context: A127132 A141764 A075744 * A261899 A109186 A099391

Adjacent sequences:  A277607 A277608 A277609 * A277611 A277612 A277613

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 23 2016

STATUS

approved

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Last modified October 15 18:54 EDT 2021. Contains 348034 sequences. (Running on oeis4.)