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A157050
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An antidiagonal integration sequence: t(n,m)=(2*n + 1)!!*(2*m + 1)!!*Integrate[Sum[x^i, {i, 0, n}]*Sum[x^j, {j, 0, m}]/2.
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0
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1, 3, 3, 20, 12, 20, 140, 75, 75, 140, 1449, 588, 495, 588, 1449, 15939, 5859, 3780, 3780, 5859, 15939, 226512, 68904, 38880, 30240, 38880, 68904, 226512, 3397680, 953667, 449955, 306180, 306180, 449955, 953667, 3397680, 61589385, 14980680
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OFFSET
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0,2
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COMMENTS
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Row sums are:
{1, 6, 52, 430, 4569, 51156, 698832, 10214964, 176319945, 3246909930, 68808711060,...}.
The central sequence is:
{1, 3, 12, 75, 495, 3780, 30240, 306180, 3161025, 37266075, 447192900, ...}.
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LINKS
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Table of n, a(n) for n=0..37.
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FORMULA
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t(n,m)=(2*n + 1)!!*(2*m + 1)!!*Integrate[Sum[x^i, {i, 0, n}]*Sum[x^j, {j, 0, m}]/2;
Out_(n,m)=antidiagonal(t(n,m)).
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EXAMPLE
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{1},
{3, 3},
{20, 12, 20},
{140, 75, 75, 140},
{1449, 588, 495, 588, 1449},
{15939, 5859, 3780, 3780, 5859, 15939},
{226512, 68904, 38880, 30240, 38880, 68904, 226512},
{3397680, 953667, 449955, 306180, 306180, 449955, 953667, 3397680},
{61589385, 14980680, 6364215, 3645180, 3161025, 3645180, 6364215, 14980680, 61589385},
{1170198315, 266158035, 98841600, 50990940, 37266075, 37266075, 50990940, 98841600, 266158035, 1170198315},
{25824101940, 5235565140, 1784729700, 807861600, 528500700, 447192900, 528500700, 807861600, 1784729700, 5235565140, 25824101940}
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MATHEMATICA
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a = Table[(2*n + 1)!!*(2*m + 1)!!*Integrate[Sum[x^i, {i, 0, n}]*Sum[ x^j, {j, 0, m}]/2, {x, -1, 1}], {n, 0, 10}, {m, 0, 10}];
b = Table[Table[a[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[a]}];
Flatten[%]
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CROSSREFS
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Sequence in context: A101617 A131443 A304562 * A059368 A090694 A078431
Adjacent sequences: A157047 A157048 A157049 * A157051 A157052 A157053
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula, Feb 22 2009
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STATUS
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approved
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