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);
A365192
G.f. satisfies A(x) = 1 + x*A(x)^5 / (1 - x*A(x)^2).
Original entry on oeis.org
1, 1, 6, 48, 443, 4445, 47107, 518835, 5880223, 68130860, 803369481, 9609294542, 116310009888, 1421951861817, 17533301767624, 217796367181117, 2722942699583650, 34236790400004432, 432649744252128084, 5492060945760586212, 69998993052214823013
Offset: 0
-
a(n) = sum(k=0, n, binomial(2*n+3*k+1, k)*binomial(n-1, 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));
A371574
G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) * (1 + x*A(x)) )^2.
Original entry on oeis.org
1, 2, 13, 106, 986, 9902, 104641, 1146654, 12910674, 148462310, 1736178005, 20584835962, 246874102771, 2989580399330, 36504669373240, 448960388422126, 5556453433915920, 69150493021938224, 864833621158491876, 10863849369160145222, 137011477676531989664
Offset: 0
-
a(n, r=2, s=1, t=5, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
Showing 1-7 of 7 results.