A381911
Expansion of (1/x) * Series_Reversion( x * (1-x) / B(x) ), where B(x) is the g.f. of A001764.
Original entry on oeis.org
1, 2, 9, 55, 394, 3102, 25969, 226891, 2045342, 18883205, 177640462, 1696658418, 16408796013, 160366113609, 1581329919636, 15713344659359, 157187582466527, 1581676730708500, 15998326150898211, 162571286470135097, 1658893916098102321, 16991130941208846890
Offset: 0
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Table[Sum[Binomial[n + 3*k + 1, k] * Binomial[2*n - k, n - k]/(n + 3*k + 1), {k, 0, n}], {n, 0, 25}] (* Vaclav Kotesovec, Mar 22 2025 *)
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a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(2*n-k, n-k)/(n+3*k+1));
A381916
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / B(x) ), where B(x) is the g.f. of A002293.
Original entry on oeis.org
1, 4, 29, 270, 2897, 34051, 426199, 5582619, 75660075, 1052748518, 14956346820, 216088986290, 3165555750458, 46912569559556, 702072705679590, 10595488626535181, 161071258091631337, 2464201011094137000, 37911236702465987337, 586166246311185676045, 9103432675706477369934
Offset: 0
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a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(4*n-k+2, n-k)/(n+4*k+1));
A381912
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / B(x) ), where B(x) is the g.f. of A001764.
Original entry on oeis.org
1, 3, 17, 124, 1038, 9470, 91586, 923542, 9608323, 102403921, 1112500651, 12275235274, 137193964646, 1549964417407, 17672282336488, 203092563108610, 2350061579393077, 27357919380212638, 320186582453226290, 3765185566095185740, 44465070300433434901, 527131055014319691537
Offset: 0
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a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(3*n-k+1, n-k)/(n+3*k+1));
Showing 1-3 of 3 results.