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A277611 Expansion of 1 / (1 - Sum_{k>=1} k^(k-2) * x^k ).

%I A277611 #18 Feb 08 2020 03:27:12
%S A277611 1,1,2,6,27,180,1678,20388,305331,5423511,111282445,2587931469,
%T A277611 67239205808,1929910531883,60636166356164,2069775112992573,
%U A277611 76268207153351225,3017346008698599752,127561003043924116908,5738904556162964523209,273764048456544759900846,13802374108958236134168506,733335098861491664742838394,40953333749038944871704984923,2398217239830108487402017089693,146949291558772355319517897103987
%N A277611 Expansion of 1 / (1 - Sum_{k>=1} k^(k-2) * x^k ).
%H A277611 Seiichi Manyama, <a href="/A277611/b277611.txt">Table of n, a(n) for n = 0..388</a>
%F A277611 a(n) ~ n^(n-2) * (1 + 2*exp(-1)/n). - _Vaclav Kotesovec_, Nov 06 2016
%F A277611 a(0) = 1; a(n) = Sum_{k=1..n} k^(k-2) * a(n-k). - _Ilya Gutkovskiy_, Feb 07 2020
%e A277611 G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 27*x^4 + 180*x^5 + 1678*x^6 + 20388*x^7 + 305331*x^8 + 5423511*x^9 + 111282445*x^10 + 2587931469*x^11 + 67239205808*x^12 +...
%e A277611 such that A(x) = 1 / (1 - Sum_{k>=1} k^(k-2) * x^k ).
%e A277611 The logarithm of the g.f. begins:
%e A277611 log(A(x)) = x + 3*x^2/2 + 13*x^3/3 + 83*x^4/4 + 746*x^5/5 + 8817*x^6/6 + 129340*x^7/7 + 2261195*x^8/8 + 45815431*x^9/9 + 1054594428*x^10/10 + 27167908186*x^11/11 + 774186515309*x^12/12 + 24174818590638*x^13/13 + 820795732075686*x^14/14 + 30104104733233598*x^15/15 +...
%e A277611 which equals the sum
%e A277611 log(A(x)) = (x + x^2 + 3*x^3 + 16*x^4 + 125*x^5 + 1296*x^6 +...) +
%e A277611 (x^2 + 2*x^3 + 7*x^4 + 38*x^5 + 291*x^6 + 2938*x^7 +...)/2 +
%e A277611 (x^3 + 3*x^4 + 12*x^5 + 67*x^6 + 507*x^7 + 5001*x^8 +...)/3 +
%e A277611 (x^4 + 4*x^5 + 18*x^6 + 104*x^7 + 783*x^8 + 7572*x^9 +...)/4 +
%e A277611 (x^5 + 5*x^6 + 25*x^7 + 150*x^8 + 1130*x^9 + 10751*x^10 +...)/5 +
%e A277611 (x^6 + 6*x^7 + 33*x^8 + 206*x^9 + 1560*x^10 + 14652*x^11 +...)/6 +
%e A277611 (x^7 + 7*x^8 + 42*x^9 + 273*x^10 + 2086*x^11 + 19404*x^12 +...)/7 +
%e A277611 ... +
%e A277611 (x + 2^0*x^2 + 3^1*x^3 + 4^2*x^4 + 5^3*x^5 +...+ k^(k-2)*x^k +...)^n/n +
%e A277611 ...
%t A277611 CoefficientList[Series[1/(1 - Sum[k^(k-2) * x^k, {k, 1, 20}]), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Nov 06 2016 *)
%o A277611 (PARI) {a(n) = polcoeff( 1/(1 - sum(k=1, n+1, k^(k-2) * x^k +x*O(x^n)) ), n)}
%o A277611 for(n=0, 30, print1(a(n), ", "))
%Y A277611 Cf. A088342, A277610.
%K A277611 nonn
%O A277611 0,3
%A A277611 _Paul D. Hanna_, Oct 23 2016