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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

Table of n, a(n) for n=0..37.

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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Last modified December 19 03:55 EST 2014. Contains 252175 sequences.