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A199749 Numerators of Bernoulli(x)^x. 0
1, 0, -1, -1, 1, 61, -23, -391, 149, 8731, -50299, -422111, 7453, 1282822973, 57034969, -20654287, -312999143, 9991318331, 1542439211, -22986862505597, -201806454439, -211506271693601, 5229666198697, 1077172798985427449, -61387659243913771, -6860376024090670391 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Table of n, a(n) for n=0..25.

FORMULA

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

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.

EXAMPLE

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 + ...

PROG

(Maxima)

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);

CROSSREFS

Sequence in context: A012860 A002108 A087409 * A303687 A033381 A204748

Adjacent sequences:  A199746 A199747 A199748 * A199750 A199751 A199752

KEYWORD

sign

AUTHOR

Vladimir Kruchinin, Nov 09 2011

STATUS

approved

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Last modified December 2 14:09 EST 2021. Contains 349445 sequences. (Running on oeis4.)