A381879
Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / C(x) ), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 3, 16, 106, 788, 6292, 52743, 457946, 4083328, 37174786, 344142192, 3229827900, 30661272627, 293907951057, 2840826401664, 27657352868946, 270968414904700, 2669604470832568, 26431802684789970, 262864480970961882, 2624640191306617088, 26301183967687772360
Offset: 0
A381882
Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 * C(x)) ), where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 4, 24, 175, 1428, 12525, 115468, 1103777, 10844715, 108860766, 1111722956, 11514401451, 120666441067, 1277161022725, 13633269293868, 146606818816257, 1586739194404521, 17271207134469417, 188942438655850740, 2076317084779878706, 22909617070555385010
Offset: 0
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
-
a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(4*n-k+2, n-k)/(n+4*k+1));
A381913
Expansion of (1/x) * Series_Reversion( x * (1-x)^3 / B(x) ), where B(x) is the g.f. of A001764.
Original entry on oeis.org
1, 4, 28, 245, 2422, 25860, 291106, 3405405, 41014131, 505344113, 6341182427, 80768735045, 1041645452650, 13575670575944, 178528253213469, 2366073408348545, 31571528771106126, 423794981085407622, 5718929869862880055, 77539914280883389432, 1055790501909183080512
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(4*n-k+2, n-k)/(n+3*k+1));
A381876
G.f. A(x) satisfies A(x) = C(x) / (1 - x*A(x))^3, where C(x) is the g.f. of A000108.
Original entry on oeis.org
1, 4, 23, 156, 1167, 9311, 77710, 670294, 5928183, 53467931, 489904745, 4547296624, 42667426369, 404044679434, 3856480309376, 37062228265769, 358330619946164, 3482936427997599, 34014454418349579, 333598711996924548, 3284326412065118717, 32446900771699499147
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+k+1, k)*binomial(4*n-4*k+2, n-k)/(n+k+1));
Showing 1-5 of 5 results.