A059587 T(n,m) = (1/m!)*Sum_{i=0..m} stirling1(m,i)*(2^i)*(2^i+1)*...*(2^i+n-1).

1, 1, 1, 2, 1, 2, 6, 7, 4, 1, 6, 24, 48, 68, 73, 56, 28, 8, 1, 24, 120, 360, 940, 2251, 4704, 8176, 11488, 12876, 11440, 8008, 4368, 1820, 560, 120, 16, 1, 120, 720, 3000, 12720, 56660, 247016, 987252, 3480536, 10647035, 28163200, 64592320, 129068160

Offset

0,4

Links

Table of n, a(n) for n=0..47.

Formula

T(n, m) = Sum_{i=0..n} |stirling1(n, i)|*binomial(2^i, m).

Example

Triangle starts:
1, 1;
1, 2, 1;
2, 6, 7, 4, 1;
6, 24, 48, 68, 73, 56, 28, 8, 1;
...

Maple

with(combinat): for n from 0 to 10 do for m from 0 to 2^n do printf(`%d, `, sum(abs(stirling1(n, i))*binomial(2^i, m), i=0..n)) od: od:

Crossrefs

Cf. A059084, (row sums) A059588.

Sequence in context: A248100 A153896 A074727 * A070236 A020825 A259992

Adjacent sequences: A059584 A059585 A059586 * A059588 A059589 A059590

Keyword

easy,nonn,tabf

Author

Vladeta Jovovic, Jan 23 2001

Extensions

More terms from James A. Sellers, Jan 24 2001

Status

approved