A014784 Triangle of numbers associated with Genocchi numbers.

1, 1, 1, 2, 3, 2, 7, 12, 12, 7, 38, 69, 81, 69, 38, 295, 552, 702, 702, 552, 295, 3098, 5901, 7857, 8559, 7857, 5901, 3098, 42271, 81444, 111618, 128034, 128034, 111618, 81444, 42271, 726734, 1411197, 1971945, 2339631, 2467665, 2339631, 1971945

Offset: 0

Author

N. J. A. Sloane

Keywords

• tabl
• nonn
• easy

Links

• G. Kreweras, Sur les permutations comptées par les nombres de Genocchi de 1-ière et 2-ième espèce, Europ. J. Comb., vol. 18, pp. 49-58, 1997.
• G. Kreweras and D. Dumont, Sur les anagrammes alternés, Discrete Mathematics, Volume 211, Issues 1-3, 28 January 2000, Pages 103-110. Zbl 0944.05003.

Crossrefs

Cf. A035003.

Columns include A000366 and A102078. Row sums are in A000366.

Programs

Mathematica

a[ 1, 1 ]=1; a[ n_, k_ ] := 0 /; (k>n || k<=0); a[ n_, 1 ]=Sum[ a[ n-1, i ], {i, 1, n-1} ] a[ n_, k_ ] := a[ n, k ]=2a[ n, k-1 ]-a[ n, k-2 ]-a[ n-1, k-1 ]-a[ n-1, k-2 ]; Flatten[ Table[ a[ n, i ], {n, 1, 10}, {i, 1, n} ] ]

Extensions

More terms from Erich Friedman.