A007188 Multiplicative encoding of Pascal triangle: Product p(i+1)^C(n,i).

2, 6, 90, 47250, 66852843750, 2806877704512541816406250, 1216935896582703898519354781702537118597533386230468750

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

n-th power of x+1 using the encoding of polynomials defined in A206284 and A297845. - Peter Munn, Jul 20 2022

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
• N. J. A. Sloane, An on-line version of the Encyclopedia of Integer Sequences, Electronic J. Combinatorics, Vol. 1, no. 1, 1994.
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Leftmost column of square array A066117.

Cf. A007318, A123098, A206295, A206284, A267096, A297845.

Programs

Mathematica

c[n_] := CoefficientList[(1 + x)^n, x]; f[n_] := Product[Prime[k]^c[n][[k]], {k, 1, Length[c[n]]}]; Table[f[n], {n, 1, 7}] (* Clark Kimberling, Feb 05 2012 *)

Formula

a(0) = 2; for n > 0, a(n) = A297845(a(n-1), 6). - Peter Munn, Jul 20 2022