A297704 Triangle read by rows, T(n,k) = binomial(n, k)*hypergeom2F1(k - n, n + 1, k + 2, -2) for n >= 0 and 0 <= k <= n.

1, 3, 1, 15, 6, 1, 93, 39, 9, 1, 645, 276, 72, 12, 1, 4791, 2073, 576, 114, 15, 1, 37275, 16242, 4689, 1020, 165, 18, 1, 299865, 131295, 38889, 8979, 1635, 225, 21, 1, 2474025, 1087080, 327960, 78888, 15510, 2448, 294, 24, 1

Offset

0,2

Links

Peter Luschny, row n for n = 0..44

Example

Triangle starts:
[0]     1
[1]     3,     1
[2]    15,     6,    1
[3]    93,    39,    9,    1
[4]   645,   276,   72,   12,   1
[5]  4791,  2073,  576,  114,  15,  1
[6] 37275, 16242, 4689, 1020, 165, 18, 1

Mathematica

T[n_, k_] := Binomial[n, k] Hypergeometric2F1[k - n, n + 1, k + 2, -2];
Table[T[n, k], {n, 0, 6}, {k, 0, n}] // Flatten

Crossrefs

T(n, 0) = A103210(n).

Row sums are A243626(n+1).

Sequence in context: A065250 A092589 A048966 * A104990 A089463 A136231

Adjacent sequences: A297701 A297702 A297703 * A297705 A297706 A297707

Keyword

nonn,tabl

Author

Peter Luschny, Jan 07 2018

Status

approved