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Search: id:A113607
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| 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 11, 11, 1, 1, 1, 1, 26, 66, 26, 1, 1, 1, 1, 57, 302, 302, 57, 1, 1, 1, 1, 120, 1191, 2416, 1191, 120, 1, 1, 1, 1, 247, 4293, 15619, 15619, 4293, 247, 1, 1, 1, 1, 502, 14608, 88234, 156190, 88234, 14608, 502, 1, 1, 1, 1, 1013
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Not entirely symmetrical, the x^(n+1)+1 polynomials was added to remove zeros and make the triangle more symmetrical.
Row sums are:
{1, 3, 3, 4, 8, 26, 122, 722, 5042, 40322, 362882, 3628802}.
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FORMULA
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f(x,n)=x^(n+1)+1+A123125(x,n).
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MATHEMATICA
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lear[f, x, n, a] f[x_, n_] := f[x, n] = x^(n + 1) + (1 - x)^(n + 1)*Sum[k^n*x^k, {k, 0, Infinity}] + 1; Table[FullSimplify[ExpandAll[f[x, n]]], {n, 0, 10}]; a = Join[{{1}}, Table[CoefficientList[FullSimplify[ExpandAll[f[x, n]]], x], {n, 0, 10}]]; Flatten[a]
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CROSSREFS
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Cf. A123125.
Sequence in context: A108465 A069347 A161606 this_sequence A082586 A160094 A043283
Adjacent sequences: A113604 A113605 A113606 this_sequence A113608 A113609 A113610
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Aug 25 2008
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