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
-
a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(3*n-k+1, n-k)/(n+3*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));
A381914
Expansion of (1/x) * Series_Reversion( x * (1-x) / B(x) ), where B(x) is the g.f. of A002293.
Original entry on oeis.org
1, 2, 10, 72, 624, 6009, 61809, 664813, 7384613, 84045565, 974913510, 11483316680, 136974177209, 1651166320547, 20083352214058, 246168280262403, 3037682020219285, 37706043912831337, 470482875049515074, 5897864081341146065, 74243055437832292562, 938101296155866961124
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(2*n-k, n-k)/(n+4*k+1));
A381905
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, 8, 47, 331, 2570, 21204, 182383, 1617163, 14675783, 135643839, 1272434069, 12083390801, 115934171020, 1122129142754, 10943574296787, 107433077283767, 1060800046515405, 10528321010319417, 104972259713887665, 1050936451974803973, 10560662821468607719
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+3*k+1, k)*binomial(n+1, n-k)/(n+3*k+1));
Showing 1-4 of 4 results.