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A141723 Triangle T(n, k) = Sum_{j=0..n} (2*n)!/((2*n-k-j)!*j!*k!), read by rows. 1
1, 3, 4, 11, 28, 24, 42, 156, 225, 160, 163, 792, 1596, 1736, 1120, 638, 3820, 9855, 14400, 13230, 8064, 2510, 17832, 55968, 102520, 122265, 100584, 59136, 9908, 81368, 300482, 661024, 968968, 1005004, 765765, 439296, 39203, 365104, 1549320, 3975440, 6910540, 8653008, 8112104, 5845840, 3294720 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

FORMULA

T(n, k) = Sum_{j=0..n} (2*n)!/((2*n-k-j)!*j!*k!).

EXAMPLE

Triangle begins as:

     1;

     3,     4;

    11,    28,     24;

    42,   156,    225,    160;

   163,   792,   1596,   1736,   1120;

   638,  3820,   9855,  14400,  13230,   8064;

  2510, 17832,  55968, 102520, 122265,  100584,  59136;

  9908, 81368, 300482, 661024, 968968, 1005004, 765765, 439296;

MATHEMATICA

Table[Sum[Multinomial[2*n-k-j, k, j], {j, 0, n}], {n, 0, 12}, {k, 0, n}]//Flatten

PROG

(Magma) F:= Factorial; [(&+[F(2*n)/(F(k)*F(j)*F(2*n-k-j)): j in [0..n]]): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 28 2021

(Sage) f=factorial; flatten([[sum(f(2*n)/(f(k)*f(j)*f(2*n-k-j)) for j in (0..n)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Mar 28 2021

CROSSREFS

Sequence in context: A198443 A041231 A042129 * A268478 A180363 A100845

Adjacent sequences:  A141720 A141721 A141722 * A141724 A141725 A141726

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Sep 12 2008

EXTENSIONS

Edited by G. C. Greubel, Mar 28 2021

STATUS

approved

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Last modified September 20 14:44 EDT 2021. Contains 347586 sequences. (Running on oeis4.)