A128322 Column 1 of triangle A128320; a(n) = A128321(n) + 2n*A128321(n-1), where A128321 is column 0 of triangle A128320.

1, 3, 8, 41, 234, 1602, 11976, 98541, 866942, 8139602, 80559456, 837863578, 9098447188, 102867879636, 1206145137840, 14632952210685, 183197674060470, 2362463132266770, 31320354882679440, 426245968192108590

Offset: 0

Author

Paul D. Hanna, Feb 25 2007

Keywords

• nonn

Crossrefs

Cf. A128320 (triangle), A128321 (column 0), A128323 (column 2), A128324 (row sums); variant: A115082.

Programs

PARI

{a(n)=sum(k=0,(n+1)\2,binomial(2*n-2*k,n-k)/(n-k+1)*binomial(2*k,k)/(k+1) *(k+1)!*binomial(n+1,2*k))}
for(n=0,25, print1(a(n),", "))

Formula

a(n) = Sum_{k=0..[(n+1)/2]} A000108(n-k)*A000108(k)*(k+1)!*C(n+1,2k) where A000108 is the Catalan numbers.

a(n) = Sum_{k=0..[(n+1)/2]} C(2(n-k),n-k)/(n-k+1)*C(2k,k)/(k+1)*(k+1)!*C(n+1,2k).