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A294621 Number of partitions of n into generalized heptagonal numbers (A085787). 3
1, 1, 1, 1, 2, 2, 2, 3, 4, 4, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 18, 20, 21, 23, 26, 29, 32, 35, 38, 41, 45, 49, 53, 59, 64, 69, 73, 80, 87, 94, 101, 109, 117, 125, 134, 145, 156, 167, 178, 190, 202, 217, 232, 249, 265, 282, 299, 318, 339, 361, 384, 408, 432, 457, 484, 514, 545, 578, 610, 646 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..70.

Eric Weisstein's World of Mathematics, Heptagonal Number

Index to sequences related to polygonal numbers

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=1} 1/((1 - x^(k*(5*k-3)/2))*(1 - x^(k*(5*k+3)/2))).

EXAMPLE

a(8) = 4 because we have [7, 1], [4, 4], [4, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1].

MATHEMATICA

nmax = 70; CoefficientList[Series[Product[1/((1 - x^(k (5 k - 3)/2)) (1 - x^(k (5 k + 3)/2))), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A007294, A085787, A095699, A279012, A294622, A294623.

Sequence in context: A025773 A308303 A285763 * A029077 A112176 A112205

Adjacent sequences:  A294618 A294619 A294620 * A294622 A294623 A294624

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 05 2017

STATUS

approved

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Last modified October 21 00:18 EDT 2021. Contains 348119 sequences. (Running on oeis4.)