A129653 Antidiagonal sums of number triangle A129652.

1, 1, 4, 15, 83, 556, 4435, 40773, 423836, 4908403, 62606297, 871421976, 13136605577, 213122669141, 3701085673676, 68480774296803, 1344611320542931, 27917413103561540, 611000785570868627, 14056645627856206809, 339081826905338009620, 8557085279980716462407

Offset: 0

Author

Paul Barry, Apr 26 2007

Keywords

• easy
• nonn

Links

• T.-X. He, A symbolic operator approach to power series transformation-expansion formulas, JIS 11 (2008) 08.2.7

Crossrefs

Cf. A129652.

Programs

PARI

a(n) = sum(k=0, n\2, ((n-k)!/k!)*sum(i=0, n-2*k, binomial(n-2*k-1,i)/(n-2*k-i)!)); \\ Michel Marcus, Sep 10 2015

Formula

a(n) = Sum_{k=0..floor(n/2)} (((n-k)!/k!)*sum{i=0..n-2k} C(n-2k-1,i)/(n-2k-i)!).