A371117
E.g.f. satisfies A(x) = 1 - x*log(1 - x*A(x)).
Original entry on oeis.org
1, 0, 2, 3, 32, 210, 2184, 26460, 373344, 6150816, 113958720, 2362345920, 54094694400, 1355708296800, 36926213869440, 1085886303989760, 34291129916574720, 1157362522046277120, 41576054625791078400, 1583864892141097098240, 63779322541075124428800
Offset: 0
-
nmax = 20; A[] = 0; Do[A[x] = 1 - x*Log[1 - x*A[x]] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] * Range[0,nmax]! (* Vaclav Kotesovec, Mar 11 2024 *)
-
a(n) = n!*sum(k=0, n\2, abs(stirling(n-k, k, 1))/(n-2*k+1)!);
A371116
E.g.f. satisfies A(x) = 1 + x^2*(exp(x*A(x)) - 1).
Original entry on oeis.org
1, 0, 0, 6, 12, 20, 750, 7602, 47096, 589752, 11823930, 169812830, 2287327812, 46793930196, 1061518458182, 21163158296490, 458344052450160, 12165772611938672, 329982890581149426, 8764089834124752822, 255655700917556204540, 8220667673623130347020
Offset: 0
-
nmax = 20; CoefficientList[Series[1 - x^2 - ProductLog[-E^(x*(1 - x^2))*x^3]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 11 2024 *)
-
a(n) = n!*sum(k=0, n\3, stirling(n-2*k, k, 2)/(n-3*k+1)!);
A371138
E.g.f. satisfies A(x) = 1 - x^2*A(x)^2*log(1 - x*A(x)).
Original entry on oeis.org
1, 0, 0, 6, 12, 40, 2340, 18648, 154560, 5767200, 95911200, 1438778880, 48014778240, 1228487644800, 27997623029376, 972327510000000, 32550437645107200, 1006902423902269440, 38894136241736494080, 1569697954634035537920, 61093442927846310912000
Offset: 0
-
a(n) = n!^2*sum(k=0, n\3, abs(stirling(n-2*k, k, 1))/((n-2*k)!*(n-k+1)!));
A371233
E.g.f. satisfies A(x) = 1 - x^2*log(1 - x*A(x)^2).
Original entry on oeis.org
1, 0, 0, 6, 12, 40, 1620, 16128, 154560, 3378240, 67828320, 1247843520, 28996704000, 773215822080, 20900234234880, 609432997219200, 19677823129036800, 674330219708221440, 24327437969162280960, 936555233579552563200, 38250260222888409292800
Offset: 0
-
a(n) = n!*sum(k=0, n\3, (2*n-4*k)!*abs(stirling(n-2*k, k, 1))/((n-2*k)!*(2*n-5*k+1)!));
A371302
E.g.f. satisfies A(x) = 1/(1 + x^2*log(1 - x*A(x))).
Original entry on oeis.org
1, 0, 0, 6, 12, 40, 1620, 13608, 117600, 2924640, 49603680, 782147520, 19083936960, 463369645440, 10836652514688, 304533583200000, 9218842256332800, 281872333420554240, 9421579421176089600, 338543319734116116480, 12590519274541116518400
Offset: 0
-
a(n) = n!*sum(k=0, n\3, (n-k)!*abs(stirling(n-2*k, k, 1))/((n-2*k)!*(n-2*k+1)!));
Showing 1-5 of 5 results.