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 A157050 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. 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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,...}. LINKS FORMULA 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)=anti-diagonal(t(n,m)). EXAMPLE {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} MATHEMATICA 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[%] CROSSREFS Sequence in context: A234018 A101617 A131443 * A059368 A090694 A078431 Adjacent sequences:  A157047 A157048 A157049 * A157051 A157052 A157053 KEYWORD nonn,tabl,uned AUTHOR Roger L. Bagula, Feb 22 2009 STATUS approved

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