A378461
a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(2*n+2*k-1,n-k).
Original entry on oeis.org
1, 2, 16, 137, 1216, 11057, 102229, 956601, 9032680, 85893860, 821402341, 7891371303, 76105710253, 736364519399, 7144586617597, 69487754788517, 677259385478616, 6613163312601491, 64681617534027028, 633569272646345064, 6214190349161222941, 61023489213944162889
Offset: 0
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a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(2*n+2*k-1, n-k));
A378465
Expansion of (1/x) * Series_Reversion( x * (1 - x - x/(1 - x)) ).
Original entry on oeis.org
1, 2, 9, 51, 324, 2206, 15737, 116098, 878495, 6780544, 53175176, 422508607, 3394004192, 27518168434, 224899980185, 1850830170355, 15324273361220, 127562500961502, 1066940307951747, 8962213871074848, 75572666059970392, 639485384767169924, 5428457500063304272
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x/(1-x)))/x)
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a(n) = sum(k=0, n, binomial(n+k, k)*binomial(2*n+k, n-k))/(n+1);
A367413
Expansion of (1/x) * Series_Reversion( x * (1-x-x^3/(1-x)^2) ).
Original entry on oeis.org
1, 1, 2, 6, 22, 87, 356, 1493, 6398, 27936, 123906, 556734, 2528668, 11590555, 53545932, 249065874, 1165482126, 5482782933, 25914899804, 123009541412, 586121731150, 2802470267460, 13441993044464, 64660400422341, 311861855749484, 1507802756171072, 7306422899878394
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^3/(1-x)^2))/x)
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a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(2*n, n-3*k))/(n+1);
Showing 1-3 of 3 results.