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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. 6
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified February 26 05:51 EST 2020. Contains 332277 sequences. (Running on oeis4.)