A365178
G.f. satisfies A(x) = 1 + x*A(x)^4*(1 + x).
Original entry on oeis.org
1, 1, 5, 30, 210, 1595, 12791, 106574, 913562, 8004861, 71375653, 645536234, 5907683486, 54605672300, 509043322720, 4780441915832, 45182744331388, 429472919087158, 4102806757542542, 39370967793387086, 379335734835510622, 3668220243145708341
Offset: 0
-
a(n) = sum(k=0, n, binomial(k, n-k)*binomial(4*k, k)/(3*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));
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));
A371578
G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) * (1 + x) )^2.
Original entry on oeis.org
1, 2, 13, 102, 916, 8880, 90607, 958794, 10426089, 115798342, 1308035135, 14980661482, 173553196140, 2030265152576, 23948922940698, 284543368174220, 3402103050539715, 40903437537402792, 494215527894112099, 5997782678374854902, 73078635875447981850
Offset: 0
-
a(n, r=2, s=1, t=5, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
A367017
G.f. satisfies A(x) = 1 + x*A(x)^5*(1 - x).
Original entry on oeis.org
1, 1, 4, 25, 185, 1495, 12776, 113534, 1038535, 9713905, 92480570, 893215584, 8730601596, 86198356180, 858388634250, 8611765147660, 86958794304735, 883103159075400, 9013769253136005, 92419535419392485, 951446700812718515, 9831013564639954705
Offset: 0
-
a(n) = sum(k=0, n, (-1)^(n-k)*binomial(k, n-k)*binomial(5*k, k)/(4*k+1));
A381940
G.f. A(x) satisfies A(x) = (1 + x) * B(x*A(x)), where B(x) is the g.f. of A002293.
Original entry on oeis.org
1, 2, 7, 51, 440, 4170, 41921, 438972, 4736281, 52286520, 587774685, 6705201456, 77426676892, 903251324476, 10629495065550, 126032922655030, 1504194199010435, 18056321542477095, 217859030049153565, 2640609137351540510, 32137554969392230950, 392580762083089376630
Offset: 0
-
a(n) = sum(k=0, n, binomial(5*k+1, k)*binomial(k+1, n-k)/(5*k+1));
Showing 1-9 of 9 results.