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A199749 Numerators of Bernoulli(x)^x. 0

%I

%S 1,0,-1,-1,1,61,-23,-391,149,8731,-50299,-422111,7453,1282822973,

%T 57034969,-20654287,-312999143,9991318331,1542439211,-22986862505597,

%U -201806454439,-211506271693601,5229666198697,1077172798985427449,-61387659243913771,-6860376024090670391

%N Numerators of Bernoulli(x)^x.

%F G.f. (x/(exp(x)-1))^x

%F a(n):=sum(m=1..n, (-1)^m*sum(k-m..n-m, (stirling1(k,m)*sum(j=1..k, ((-1)^(j-k)*stirling2(n-m+j,j))/((k-j)!*(n-m+j)!))))), a(0)=1.

%e A(x)=1- x^2/2 - x^3/24 + x^4/8 + 61*x^5/2880 - 23*x^6/1152 - 391*x^7/72576 + 149*x^8/69120 + 8731*x^9/9676800 - 50299*x^10/348364800 + ...

%o (Maxima)

%o a(n):=if n=0 then 1 else sum((-1)^m*sum((stirling1(k,m)*sum(((-1)^(j-k)*stirling2(n-m+j,j))/((k-j)!*(n-m+j)!),j,1,k)),k,m,n-m),m,1,n);

%K sign

%O 0,6

%A _Vladimir Kruchinin_, Nov 09 2011

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Last modified January 21 14:37 EST 2022. Contains 350479 sequences. (Running on oeis4.)