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A055325
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Matrix inverse of Euler's triangle A008292.
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4
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1, -1, 1, 3, -4, 1, -23, 33, -11, 1, 425, -620, 220, -26, 1, -18129, 26525, -9520, 1180, -57, 1, 1721419, -2519664, 905765, -113050, 5649, -120, 1, -353654167, 517670461, -186123259, 23248085, -1166221, 25347, -247, 1, 153923102577
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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LINKS
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EXAMPLE
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Triangle starts:
[1] 1;
[2] -1, 1;
[3] 3, -4, 1;
[4] -23, 33, -11, 1;
[5] 425, -620, 220, -26, 1;
[6] -18129, 26525, -9520, 1180, -57, 1;
[7] 1721419, -2519664, 905765, -113050, 5649, -120, 1;
[8]-353654167, 517670461, -186123259, 23248085, -1166221, 25347, -247, 1;
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MAPLE
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A008292:= proc(n, k) option remember;
if k < 1 or k > n then 0
elif k = 1 or k = n then 1
else (k*procname(n-1, k)+(n-k+1)*procname(n-1, k-1))
fi
end proc:
T:= Matrix(10, 10, (i, j) -> A008292(i, j)):
R:= T^(-1):
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MATHEMATICA
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m = 10 (*rows*);
t[n_, k_] := Sum[(-1)^j*(k-j)^n*Binomial[n+1, j], {j, 0, k}];
M = Array[t, {m, m}] // Inverse;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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