A340262 - OEIS

A340262

T(n, k) = multinomial(n + k/2; n, k/2) if k is even else 0. Triangle read by rows, for 0 <= k <= n.

1, 1, 0, 1, 0, 3, 1, 0, 4, 0, 1, 0, 5, 0, 15, 1, 0, 6, 0, 21, 0, 1, 0, 7, 0, 28, 0, 84, 1, 0, 8, 0, 36, 0, 120, 0, 1, 0, 9, 0, 45, 0, 165, 0, 495, 1, 0, 10, 0, 55, 0, 220, 0, 715, 0, 1, 0, 11, 0, 66, 0, 286, 0, 1001, 0, 3003, 1, 0, 12, 0, 78, 0, 364, 0, 1365, 0, 4368, 0

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OFFSET

0,6

LINKS

Table of n, a(n) for n=0..77.

EXAMPLE

Triangle starts:

[0] 1;

[1] 1, 0;

[2] 1, 0, 3;

[3] 1, 0, 4, 0;

[4] 1, 0, 5, 0, 15;

[5] 1, 0, 6, 0, 21, 0;

[6] 1, 0, 7, 0, 28, 0, 84;

[7] 1, 0, 8, 0, 36, 0, 120, 0;

[8] 1, 0, 9, 0, 45, 0, 165, 0, 495;

[9] 1, 0, 10, 0, 55, 0, 220, 0, 715, 0;

MAPLE

T := proc(n, k) `if`(k::even, combinat:-multinomial(n + k/2, n, k/2), 0) end:

seq(seq(T(n, k), k=0..n), n=0..11);

MATHEMATICA

multinomial[n_, k_List] := n!/Times @@ (k!);

T[n_, k_] := If[EvenQ[k], multinomial[n + k/2, {n, k/2}], 0];

Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, May 18 2024 *)

CROSSREFS

Cf. A130746, A067147.

Sequence in context: A166407 A285123 A159059 * A346369 A127569 A117372

Adjacent sequences: A340259 A340260 A340261 * A340263 A340264 A340265

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Jan 05 2021

STATUS

approved