A108032 Triangle T(n,k), 0<=k<=n, read by rows, defined by : T(0,0) = 1, T(n,k) = 0 if n<k or if k<0, T(n,k) = k*T(n-1, k-1) + (2n-2k-1)*T(n-1, k).

1, 1, 1, 3, 2, 2, 15, 9, 6, 6, 105, 60, 36, 24, 24, 945, 525, 300, 180, 120, 120, 10395, 5670, 3150, 1800, 1080, 720, 720, 135135, 72765, 39690, 22050, 12600, 7560, 5040, 5040, 2027025, 1081080, 582120, 317520, 176400, 100800, 60480, 40320, 40320

Offset

0,4

Links

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

Formula

Sum{ k, 0<=k<=n} T(n, k) = A034430(n).

T(n, k) = A001147(n-k)*k!*binomial(n, k).

E.g.f.: 1/(1-t*x)*1/sqrt(1-2*x) = 1 + x*(1+t) + x^2/2!*(3+2*t+2*t^2) + .... - Peter Bala, Jun 27 2012

Example

1;
1, 1;
3, 2, 2;
15, 9, 6, 6;
105, 60, 36, 24, 24; ...

Crossrefs

Diagonals : A001147, A001193, A000142.

Cf. A034430 (row sums).

Sequence in context: A266004 A206703 A122101 * A053370 A016458 A372345

Adjacent sequences: A108029 A108030 A108031 * A108033 A108034 A108035

Keyword

nonn,easy,tabl

Author

Philippe Deléham, Jun 01 2005

Status

approved