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Search: id:A112339
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| A112339 |
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Triangle read by rows of numbers b_{n,k}, n>=2, 1<=k<n such that (1/(1-q t)) prod_{n,k} 1/(1-q^n t^k)^{b_{n,k}} = sum_{i,j>=1} S_{i,j} q^i t^j where S_{i,j} are entries in the table A008277 (the inverse Euler transformation of the table of Stirling numbers of the second kind). |
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+0
2
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| 1, 1, 2, 1, 5, 3, 1, 13, 16, 4, 1, 28, 67, 34, 5, 1, 60, 249, 229, 65, 6, 1, 123, 853, 1265, 609, 107, 7, 1, 251, 2787, 6325, 4696, 1376, 168, 8, 1, 506, 8840, 29484, 31947, 14068, 2772, 244, 9, 1, 1018, 27503, 131402, 199766, 124859, 36252, 5118, 345, 10
(list; table; graph; listen)
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OFFSET
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2,3
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COMMENT
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1; 1, 2; 1, 5, 3; 1, 13, 16, 4, 1; ... Row sums equal to A085686 second column = A084174 - 1
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MAPLE
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EULERitable:=proc(tbl) local ser, out, i, j, tmp; ser:=1+add(add(q^i*t^j*tbl[i][j], j=1..nops(tbl[i])), i=1..nops(tbl)); out:=[]; for i from 1 to nops(tbl) do tmp:=coeff(ser, q, i); ser:=expand(ser*mul(add((-q^i*t^j)^k*choose(abs(coeff(tmp, t, j)), k), k=0..nops(tbl)/i), j = 1..degree(tmp, t))); ser:=subs({seq(q^j=0, j=nops(tbl)+1..degree(ser, q))}, ser); out:=[op(out), [seq(abs(coeff(tmp, t, j)), j=1..degree(tmp, t))]]; end do; out; end: EULERitable([seq([seq(combinat[stirling2](n, k), k=1..n)], n=1..11)]);
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CROSSREFS
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Cf. A008277, A085686, A112340.
Sequence in context: A125171 A048472 A038622 this_sequence A132808 A135233 A125170
Adjacent sequences: A112336 A112337 A112338 this_sequence A112340 A112341 A112342
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KEYWORD
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nonn,tabl
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AUTHOR
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Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Sep 05 2005
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