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Search: id:A128322
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| 1, 3, 8, 41, 234, 1602, 11976, 98541, 866942, 8139602, 80559456, 837863578, 9098447188, 102867879636, 1206145137840, 14632952210685, 183197674060470, 2362463132266770, 31320354882679440, 426245968192108590
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OFFSET
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0,2
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FORMULA
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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).
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PROGRAM
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(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))}
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CROSSREFS
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Cf. A128320 (triangle), A128321 (column 0), A128323 (column 2), A128324 (row sums); variant: A115082.
Sequence in context: A107991 A007175 A152394 this_sequence A038048 A051763 A074435
Adjacent sequences: A128319 A128320 A128321 this_sequence A128323 A128324 A128325
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Feb 25 2007
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