A375949
Expansion of e.g.f. 1 / (4 - 3 * exp(x))^(4/3).
Original entry on oeis.org
1, 4, 32, 368, 5520, 102064, 2242832, 57095728, 1652211600, 53559908784, 1922581295632, 75700072208688, 3243905700776080, 150289130386531504, 7485459789379535632, 398857142195958963248, 22639650637589839298960, 1363772478150606703714224
Offset: 0
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nmax=17; CoefficientList[Series[1 / (4 - 3 * Exp[x])^(4/3),{x,0,nmax}],x]*Range[0,nmax]! (* Stefano Spezia, Sep 03 2024 *)
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a007559(n) = prod(k=0, n-1, 3*k+1);
a(n) = sum(k=0, n, a007559(k+1)*stirling(n, k, 2));
A375954
Expansion of e.g.f. 1 / (3 - 2 * exp(x))^(5/2).
Original entry on oeis.org
1, 5, 40, 425, 5605, 88100, 1606015, 33291725, 773093830, 19875432575, 560334083965, 17187010139150, 569768238573805, 20299523526975425, 773470729977309040, 31385122689116278325, 1351135296804805544905, 61507193821772778512900
Offset: 0
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nmax=17; CoefficientList[Series[1 / (3 - 2 * Exp[x])^(5/2),{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+2)*stirling(n, k, 2))/3;
A375991
Expansion of e.g.f. (3 - 2 * exp(x))^(3/2).
Original entry on oeis.org
1, -3, 0, 9, 45, 252, 1935, 19989, 260190, 4063887, 73823445, 1527002694, 35408499885, 909389617497, 25618701424680, 785355764569749, 26024092206299505, 926859918577582332, 35306305954587340515, 1432301360556686816529, 61649353087003554947550
Offset: 0
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With[{nn=20},CoefficientList[Series[(3-2Exp[x])^(3/2),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 19 2025 *)
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a(n) = sum(k=0, n, prod(j=0, k-1, 2*j-3)*stirling(n, k, 2));
Showing 1-3 of 3 results.