A128254 Erroneous version of A103450.

1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 7, 12, 7, 1, 1, 9, 22, 22, 9, 1, 1, 11, 35, 50, 35, 11, 11, 13, 51, 95, 95, 51, 13, 1, 1, 15, 70, 161, 210, 161, 70, 15, 1, 1, 17, 92, 252, 406, 406, 252, 92, 17, 1

Offset

1,5

Comments

The triangle is bisymmetric, row sums = A045623: (1, 2, 5, 12, 28, 64,...). A114219(signed) * A007318 = A128255.

Links

Table of n, a(n) for n=1..54.

Formula

A007318 * A114219, where the latter is signed: {1; 0,1; 0,1,1; 0,-1,2,1; 0,1,-2,3,1;...}. The signed version of A114219 = A097807 * A128229.

T(n,k) = k Binomial[n-2,k-1] + Binomial[n-2,k-2], for 1 <= k <= n. - O. D'Antona, Dec 17 2007

Example

First few rows of the triangle are:
1;
1, 1;
1, 3, 1;
1, 5, 5, 1;
1, 7, 12, 7, 1;
1, 9, 22, 22, 9, 1;
1, 11, 35, 50, 35, 11, 1;
...
Central coefficients T(2n,n) = A141222. - Emanuele Munarini, Jun 01 2012

Prog

(Maxima) T(n, k):=k*binomial(n-2, k-1)+binomial(n-2, k-2);
create_list(T(n+1, k+1), n, 0, 30, k, 0, n); [Emanuele Munarini, Jun 01 2012]

Crossrefs

Cf. A128229, A007318, A114219, A128255, A045623, A141222.

Sequence in context: A109128 A113245 A103450 * A277930 A026714 A008288

Adjacent sequences: A128251 A128252 A128253 * A128255 A128256 A128257

Keyword

dead

Author

Gary W. Adamson, Feb 20 2007

Extensions

Typo in sequence corrected by O. D'Antona (dantona(AT)dico.unimi.it), Dec 17 2007

Status

approved