A375613 Triangle read by rows: T(n, k) = n! * 4^k * hypergeom([-k], [-n], 1/4).

1, 1, 5, 2, 9, 41, 6, 26, 113, 493, 24, 102, 434, 1849, 7889, 120, 504, 2118, 8906, 37473, 157781, 720, 3000, 12504, 52134, 217442, 907241, 3786745, 5040, 20880, 86520, 358584, 1486470, 6163322, 25560529, 106028861, 40320, 166320, 686160, 2831160, 11683224, 48219366, 199040786, 821723673, 3392923553

Offset

0,3

Links

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

Formula

T(n, k) = Sum_{j=0..k} 4^(k - j)*binomial(k, k - j)*(n - j)!.

Example

Triangle starts:
[0] 1;
[1] 1, 5;
[2] 2, 9, 41;
[3] 6, 26, 113, 493;
[4] 24, 102, 434, 1849, 7889;
[5] 120, 504, 2118, 8906, 37473, 157781;
[6] 720, 3000, 12504, 52134, 217442, 907241, 3786745;
[7] 5040, 20880, 86520, 358584, 1486470, 6163322, 25560529, 106028861;
...

Mathematica

T[n_, k_] := Sum[4^(k - j)*Binomial[k, k - j]*(n - j)!, {j, 0, k}];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten

Crossrefs

Cf. A375612, A000142, A056545 (main diagonal).

Cf. A374427, A374428, A375446, A375447, A375597, A375600.

Sequence in context: A257513 A276849 A367210 * A127098 A127097 A040024

Adjacent sequences: A375610 A375611 A375612 * A375614 A375615 A375616

Keyword

nonn,tabl

Author

Detlef Meya, Aug 21 2024

Status

approved