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A230253
Coefficients of power series A(x) such that coefficient of x^n in A(x)^(n+1) equals (n+1)*(n+2)!/2 for n>=0.
1
1, 3, 3, 6, 27, 162, 1206, 10476, 103059, 1125738, 13473378, 174997908, 2448791838, 36706645908, 586646510796, 9957100024152, 178868488496643, 3390603439026618, 67639341903290730, 1416612563019545220, 31079692422132040170, 712855563504590236860, 17061654943814209044660
OFFSET
0,2
FORMULA
[x^n] A(x)^n = A111546(n) for n>=0.
EXAMPLE
G.f. A(x) = 1 + 3*x + 3*x^2 + 6*x^3 + 27*x^4 + 162*x^5 + 1206*x^6 +...
The coefficients in A(x)^n begin:
n=1: [(1),3, 3, 6, 27, 162, 1206, 10476, 103059, ...];
n=2: [1, (6), 15, 30, 99, 522, 3582, 29484, 278883, ...];
n=3: [1, 9, (36), 99, 297, 1323, 8208, 63342, 572751, ...];
n=4: [1, 12, 66, (240), 783, 3132, 17298, 123552, 1060155, ...];
n=5: [1, 15, 105, 480, (1800), 7083, 35415, 231660, 1869885, ...];
n=6: [1, 18, 153, 846, 3672, (15120), 71415, 428490, 3226797, ...];
n=7: [1, 21, 210, 1365, 6804, 30240,(141120), 789939, 5529573, ...];
n=8: [1, 24, 276, 2064, 11682, 56736, 270720,(1451520), 9485343, ...];
n=9: [1, 27, 351, 2970, 18873, 100440, 500904, 2643840,(16329600), ...]; ...
where the coefficient of x^n in A(x)^(n+1) equals (n+1)*(n+2)!/2 for n>=0.
Notice that the diagonal above the main diagonal forms A111546.
PROG
(PARI) {a(n)=polcoeff(x/serreverse(sum(m=1, n+1, (m+1)!/2*x^m)+x^2*O(x^n)), n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 13 2013
STATUS
approved