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));
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));
A365188
G.f. satisfies A(x) = 1 + x*A(x)^5*(1 + x*A(x)^4).
Original entry on oeis.org
1, 1, 6, 49, 465, 4807, 52533, 596936, 6981798, 83497115, 1016367737, 12550853210, 156845913315, 1979870172453, 25207383853375, 323325558146400, 4174108907656633, 54195445136831670, 707225283913589280, 9270735916525207605, 122020617365557674605
Offset: 0
-
a(n) = sum(k=0, n, binomial(4*n+k+1, k)*binomial(k, n-k)/(4*n+k+1));
A366980
G.f. satisfies A(x) = 1 + x*A(x)^5 * (1 - x*A(x)).
Original entry on oeis.org
1, 1, 4, 24, 171, 1336, 11060, 95298, 845649, 7675398, 70921457, 664905445, 6309060313, 60473691666, 584684295383, 5695312881404, 55839455579659, 550621231581791, 5457218248143692, 54332533436452743, 543148496962279730, 5449742750024662824
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n+4*k+1, k)*binomial(k, n-k)/(n+4*k+1));
Showing 1-6 of 6 results.