A091150 Triangle, read by rows, where the n-th row lists the coefficients of the polynomial of degree n that generates the n-th diagonal of this sequence.

1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 9, 9, 4, 1, 1, 24, 29, 16, 5, 1, 1, 76, 103, 67, 25, 6, 1, 1, 279, 405, 298, 129, 36, 7, 1, 1, 1156, 1757, 1414, 693, 221, 49, 8, 1, 1, 5300, 8355, 7177, 3889, 1396, 349, 64, 9, 1, 1, 26541, 43229, 39016, 22881, 9096, 2539, 519, 81, 10, 1, 1

Offset

0,5

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1080

Formula

T(n+k, k) = Sum T(n, j)*k^j {j=0..n}, with T(n, 0)=T(0, n)=1 for n>=0.

Example

For row n=3, k=2, T(n+k,k)=T(5,2)=29=(1)+(4)2+(3)2^2+(1)2^3.
For n=4, k=3, T(n+k,k)=T(7,3)=298=(1)+(9)3+(9)3^2+(4)3^3+(1)3^4.
Rows begin with n=0:
1;
1, 1;
1, 2, 1;
1, 4, 3, 1;
1, 9, 9, 4, 1;
1, 24, 29, 16, 5, 1;
1, 76, 103, 67, 25, 6, 1;
1, 279, 405, 298, 129, 36, 7, 1;
1, 1156, 1757, 1414, 693, 221, 49, 8, 1;
1, 5300, 8355, 7177, 3889, 1396, 349, 64, 9, 1;
1, 26541, 43229, 39016, 22881, 9096, 2539, 519, 81, 10, 1;
1, 143914, 241677, 227074, 141613, 61331, 18901, 4278, 737, 100, 11, 1;
1, 839638, 1451103, 1412233, 924257, 429396, 144349, 35890, 6793, 1009, 121, 12, 1; ...

Prog

(PARI) {T(n, k)=if(n<k||k<0, 0, if(n==k||k==0, 1, sum(j=0, n-k, T(n-k, j)*k^j)))}
for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print(""))

Crossrefs

Cf. A091151.

Sequence in context: A117418 A101494 A125781 * A091351 A058730 A112705

Adjacent sequences: A091147 A091148 A091149 * A091151 A091152 A091153

Keyword

nonn,tabl

Author

Paul D. Hanna, Dec 22 2003

Status

approved