A375597 Triangle read by rows: T(n, k) = n! * 3^k * hypergeom([-k], [-n], -2/3).

1, 1, 1, 2, 4, 10, 6, 14, 34, 82, 24, 60, 152, 388, 1000, 120, 312, 816, 2144, 5656, 14968, 720, 1920, 5136, 13776, 37040, 99808, 269488, 5040, 13680, 37200, 101328, 276432, 755216, 2066032, 5659120, 40320, 110880, 305280, 841440, 2321664, 6412128, 17725952, 49045792, 135819136

Offset

0,4

Links

Table of n, a(n) for n=0..44.

Formula

T(n, k) = (-2)^k*Sum_{j=0..k} (-3/2)^(k - j)*binomial(k, k - j)*(n - j)!.

Example

Triangle starts:
[0] 1;
[1] 1, 1;
[2] 2, 4, 10;
[3] 6, 14, 34, 82;
[4] 24, 60, 152, 388, 1000;
[5] 120, 312, 816, 2144, 5656, 14968;
[6] 720, 1920, 5136, 13776, 37040, 99808, 269488;
[7] 5040, 13680, 37200, 101328, 276432, 755216, 2066032, 5659120;
...

Mathematica

T[n_, k_] := (-2)^k*Sum[(-3/2)^(k - j)*Binomial[k, k - j]*(n - j)!, {j, 0, k}];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

Crossrefs

Cf. A375600, A000142.

Cf. A374427, A374428, A375446, A375447.

Sequence in context: A098556 A159585 A130334 * A320537 A331708 A227289

Adjacent sequences: A375594 A375595 A375596 * A375598 A375599 A375600

Keyword

nonn,tabl

Author

Detlef Meya, Aug 20 2024

Status

approved