A375948
Expansion of e.g.f. 1 / (3 - 2 * exp(x))^(3/2).
Original entry on oeis.org
1, 3, 18, 153, 1683, 22698, 362403, 6683463, 139787568, 3269240883, 84535585263, 2394699999948, 73749495626253, 2453332830142743, 87667856626175298, 3349116499958627733, 136209377351085310863, 5875794769594996985778, 267968680043585007829383
Offset: 0
-
nmax=18; CoefficientList[Series[1 / (3 - 2 * Exp[x])^(3/2),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)
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a001147(n) = prod(k=0, n-1, 2*k+1);
a(n) = sum(k=0, n, a001147(k+1)*stirling(n, k, 2));
A375952
Expansion of e.g.f. 1 / (4 - 3 * exp(x))^(5/3).
Original entry on oeis.org
1, 5, 45, 565, 9085, 177925, 4106445, 109105365, 3279219485, 109983317925, 4071784884845, 164919693538165, 7253726995805885, 344284133391481925, 17538600019076063245, 954467594134586386965, 55263075631036363208285, 3391909484128563111709925
Offset: 0
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nmax=17; CoefficientList[Series[1 / (4 - 3 * Exp[x])^(5/3),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)
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a008544(n) = prod(k=0, n-1, 3*k+2);
a(n) = sum(k=0, n, a008544(k+1)*stirling(n, k, 2))/2;
A375992
Expansion of e.g.f. (4 - 3 * exp(x))^(4/3).
Original entry on oeis.org
1, -4, 0, 16, 112, 976, 11760, 184656, 3566192, 81556176, 2152839920, 64389871696, 2151410517872, 79406805184976, 3208188040810480, 140812644820877136, 6671575179144279152, 339348322285418119376, 18443287953728909235440, 1066619199816333440144976
Offset: 0
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a(n) = sum(k=0, n, prod(j=0, k-1, 3*j-4)*stirling(n, k, 2));
A375993
Expansion of e.g.f. (4 - 3 * exp(x))^(5/3).
Original entry on oeis.org
1, -5, 5, 35, 165, 1075, 10805, 152035, 2719365, 58547475, 1469512405, 42082036035, 1353220758565, 48264167285875, 1890433757030005, 80656857839376035, 3723074712045197765, 184851684577600696275, 9822823990059902723605, 556226222504163445932035
Offset: 0
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a(n) = sum(k=0, n, prod(j=0, k-1, 3*j-5)*stirling(n, k, 2));
Showing 1-4 of 4 results.