A365184
G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x).
Original entry on oeis.org
1, 1, 6, 45, 395, 3775, 38146, 400826, 4335455, 47951065, 539823620, 6165377836, 71261299056, 831990025420, 9797505040130, 116235417614900, 1387958781395535, 16668362761081560, 201190667288072005, 2439418470063468505, 29698136499328762445
Offset: 0
-
a(n) = sum(k=0, n, binomial(k, n-k)*binomial(5*k, k)/(4*k+1));
A365189
G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^5).
Original entry on oeis.org
1, 1, 6, 50, 485, 5130, 57391, 667777, 7999095, 97986680, 1221813880, 15456556791, 197887386913, 2559189842240, 33383097891135, 438714241508615, 5803049210371375, 77199163872173757, 1032215519193531310, 13864180990526161995, 186975433988014039830
Offset: 0
-
a(n) = sum(k=0, n\2, binomial(n-k, k)*binomial(5*n+1, n-k))/(5*n+1);
A365186
G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^2).
Original entry on oeis.org
1, 1, 6, 47, 428, 4241, 44407, 483358, 5414618, 62014112, 722870120, 8547768832, 102284029963, 1236274747490, 15070955944288, 185089043535730, 2287843817573898, 28440852786725695, 355345599519983962, 4459821165693379625, 56200963128262312342
Offset: 0
-
a(n) = sum(k=0, n, binomial(2*n+3*k+1, k)*binomial(k, n-k)/(2*n+3*k+1));
A365185
G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)).
Original entry on oeis.org
1, 1, 6, 46, 411, 3996, 41062, 438662, 4823133, 54221518, 620404859, 7201317005, 84590041441, 1003656037278, 12010861830069, 144804336388912, 1757106190680819, 21443109365898743, 263009775111233392, 3240530659303505547, 40088688455992604594
Offset: 0
-
a(n) = sum(k=0, n, binomial(n+4*k+1, k)*binomial(k, n-k)/(n+4*k+1));
A365187
G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^3).
Original entry on oeis.org
1, 1, 6, 48, 446, 4511, 48218, 535800, 6127598, 71648868, 852668952, 10293847592, 125759270354, 1551872951050, 19314892116764, 242182938963024, 3056337851481678, 38790948190319404, 494825459824571528, 6340628082364678016, 81577931200018721464
Offset: 0
-
a(n) = sum(k=0, n, binomial(3*n+2*k+1, k)*binomial(k, n-k)/(3*n+2*k+1));
A376326
Expansion of (1/x) * Series_Reversion( x * (1-x-x^2)^4 ).
Original entry on oeis.org
1, 4, 30, 272, 2737, 29380, 329614, 3818540, 45329440, 548511612, 6740687924, 83898110660, 1055441468145, 13398494365088, 171422870731600, 2208161418665872, 28614197357895055, 372754395074051500, 4878709294080115494, 64123505084010848580, 846018700129069313495
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x-x^2)^4)/x)
-
a(n, s=2, t=4, u=0) = sum(k=0, n\s, binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
Showing 1-6 of 6 results.